On Low Tree-Depth Decompositions
The theory of sparse structures usually uses tree like structures as building blocks. In the context of sparse/dense dichotomy this role is played by graphs with bounded tree-depth. In this paper we survey results related to this concept and particularly explain how these graphs are used to decompos...
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| Published in: | Graphs and combinatorics Vol. 31; no. 6; pp. 1941 - 1963 |
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| Language: | English |
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01-11-2015
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| Abstract | The theory of sparse structures usually uses tree like structures as building blocks. In the context of sparse/dense dichotomy this role is played by graphs with bounded tree-depth. In this paper we survey results related to this concept and particularly explain how these graphs are used to decompose and construct more complex graphs and structures. In more technical terms we survey some of the properties and applications of low tree-depth decomposition of graphs. |
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| AbstractList | The theory of sparse structures usually uses tree like structures as building blocks. In the context of sparse/dense dichotomy this role is played by graphs with bounded tree-depth. In this paper we survey results related to this concept and particularly explain how these graphs are used to decompose and construct more complex graphs and structures. In more technical terms we survey some of the properties and applications of low tree-depth decomposition of graphs. |
| Author | Ossona de Mendez, Patrice Nešetřil, Jaroslav |
| Author_xml | – sequence: 1 givenname: Jaroslav surname: Nešetřil fullname: Nešetřil, Jaroslav organization: Computer Science Institute of Charles University (IUUK and ITI) – sequence: 2 givenname: Patrice surname: Ossona de Mendez fullname: Ossona de Mendez, Patrice email: pom@ehess.fr organization: Centre d’Analyse et de Mathématiques Sociales (CNRS, UMR 8557), Computer Science Institute of Charles University (IUUK) |
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| Cites_doi | 10.1023/B:ORDE.0000026489.93166.cb 10.1145/1379759.1379763 10.1006/jctb.1994.1052 10.1016/j.jctb.2003.09.001 10.1016/j.ejc.2005.01.010 10.1016/0890-5401(90)90043-H 10.1016/j.apal.2004.01.007 10.1016/j.ejc.2006.07.014 10.1016/j.disc.2009.04.032 10.1016/j.ejc.2011.01.006 10.1016/j.ejc.2011.09.014 10.1016/j.dam.2011.07.017 10.1016/j.ejc.2007.11.019 10.1307/mmj/1028998975 10.1002/jgt.3190160509 10.1145/210332.210337 10.1007/s00493-004-0010-2 10.1016/0012-365X(78)90178-4 10.1093/acprof:oso/9780198528173.001.0001 10.1016/j.jctb.2006.07.001 10.1016/j.ejc.2011.03.007 10.1016/j.disc.2008.03.024 10.1006/jctb.1993.1027 10.1016/j.ejc.2006.07.013 10.1016/S0747-7171(08)80013-2 10.1016/S0195-6698(03)00064-7 10.1016/0012-365X(79)90077-3 10.1017/S0963548303005741 10.7155/jgaa.00014 10.1016/0304-3975(91)90020-3 10.1007/BF02762708 10.1090/S0002-9904-1946-08715-7 10.1007/BF01305230 10.1016/j.dam.2012.03.015 10.1007/978-3-642-27875-4 10.1007/978-3-642-22953-4_19 10.1007/978-3-642-39206-1_57 10.1145/1132516.1132575 10.2168/LMCS-11(1:19)2015 10.1007/978-3-642-03816-7_33 10.1007/3-540-59071-4 10.1145/2591796.2591851 10.1007/3-540-57785-8_187 10.1007/978-3-642-32589-2_38 10.1007/978-88-7642-525-7_6 10.1007/3-540-53832-1_28 10.1007/978-3-540-70583-3_4 10.1145/2499483 10.1145/2463664.2463667 10.1016/0020-0190(89)90161-0 10.1109/LICS.2012.37 10.1007/s004530010020 10.1002/jgt.20522 10.1007/978-3-642-55566-4_29 |
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| Keywords | Classes with bounded expansion Graph decomposition 05C75 Nowhere dense classes 05C85 Model checking Low tree-depth decomposition 05C70 Homomorphism duality Tree-depth 05C15 |
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| References | Alon, Yuster, Zwick (CR4) 1995; 42 Fiorenzi, Ochem, Ossona de Mendez, Zhu (CR25) 2011; 159 Nešetřil, Shelah (CR56) 2003; 24 Borodin (CR7) 1979; 25 CR39 CR38 CR36 Dvořák, Giannopoulou, Thilikos (CR16) 2012; 33 CR34 CR33 CR32 Nešetřil, Ossona de Mendez (CR50) 2008; 29 Nešetřil, Ossona de Mendez (CR52) 2011; 32 Kierstead, Yang (CR40) 2003; 20 Alon, Mohar, Sanders (CR3) 1994; 94 Nešetřil, Ossona de Mendez (CR49) 2008; 29 Zhu (CR66) 2009; 309 Alon, McDiarmid, Reed (CR2) 1992; 12 CR6 Eggan (CR18) 1963; 10 CR5 Chrobak, Eppstein (CR8) 1991; 86 DeVos, Ding, Oporowski, Sanders, Reed, Seymour, Vertigan (CR13) 2004; 91 CR46 CR45 Nešetřil, Ossona de Mendez (CR51) 2011; 32 CR42 Jensen, Toft (CR37) 2011 Naserasr, Nigussie, Škrekovski (CR44) 2009; 309 Nešetřil, Ossona de Mendez (CR48) 2008; 29 Rossman (CR59) 2008; 55 Hell, Nešetřil (CR35) 2004 Sampathkumar (CR60) 1977; 6 Naserasr (CR43) 2007; 97 CR19 CR17 Ding (CR14) 1992; 16 CR15 CR58 CR57 CR12 CR11 CR54 CR53 Giannopoulou, Thilikos (CR30) 2012; 160 Alon, Krivelevich, Sudakov (CR1) 2003; 12 Vizing (CR64) 1976; 29 Frick, Grohe (CR26) 2004; 130 Thomassen (CR63) 1994; 62 Erdös, Stone (CR24) 1946; 52 Nešetřil, Poljak (CR55) 1985; 26 CR29 CR28 Golumbic (CR31) 1978; 24 Coppersmith, Winograd (CR9) 1990; 9 CR27 Nešetřil, Ossona de Mendez (CR47) 2006; 27 CR23 CR22 CR65 CR20 CR61 Seymour, Thomas (CR62) 1993; 58 Eppstein (CR21) 1999; 3 Courcelle (CR10) 1990; 85 Kühn, Osthus (CR41) 2004; 24 1569_CR32 1569_CR33 R Naserasr (1569_CR44) 2009; 309 1569_CR38 1569_CR39 M Golumbic (1569_CR31) 1978; 24 1569_CR36 1569_CR34 P Hell (1569_CR35) 2004 A Giannopoulou (1569_CR30) 2012; 160 N Alon (1569_CR3) 1994; 94 V Vizing (1569_CR64) 1976; 29 1569_CR65 1569_CR22 1569_CR20 T Jensen (1569_CR37) 2011 N Alon (1569_CR1) 2003; 12 J Nešetřil (1569_CR55) 1985; 26 1569_CR61 X Zhu (1569_CR66) 2009; 309 1569_CR29 N Alon (1569_CR4) 1995; 42 1569_CR27 1569_CR28 M Chrobak (1569_CR8) 1991; 86 1569_CR23 C Thomassen (1569_CR63) 1994; 62 J Nešetřil (1569_CR47) 2006; 27 R Naserasr (1569_CR43) 2007; 97 J Nešetřil (1569_CR52) 2011; 32 1569_CR54 E Sampathkumar (1569_CR60) 1977; 6 1569_CR11 1569_CR53 Z Dvořák (1569_CR16) 2012; 33 1569_CR19 J Nešetřil (1569_CR49) 2008; 29 O Borodin (1569_CR7) 1979; 25 H Kierstead (1569_CR40) 2003; 20 1569_CR17 1569_CR58 1569_CR15 1569_CR12 1569_CR57 D Eppstein (1569_CR21) 1999; 3 L Eggan (1569_CR18) 1963; 10 G Ding (1569_CR14) 1992; 16 N Alon (1569_CR2) 1992; 12 P Seymour (1569_CR62) 1993; 58 J Nešetřil (1569_CR51) 2011; 32 D Kühn (1569_CR41) 2004; 24 1569_CR42 B Courcelle (1569_CR10) 1990; 85 M Frick (1569_CR26) 2004; 130 D Coppersmith (1569_CR9) 1990; 9 J Nešetřil (1569_CR48) 2008; 29 1569_CR45 J Nešetřil (1569_CR50) 2008; 29 1569_CR46 B Rossman (1569_CR59) 2008; 55 M DeVos (1569_CR13) 2004; 91 1569_CR5 1569_CR6 F Fiorenzi (1569_CR25) 2011; 159 J Nešetřil (1569_CR56) 2003; 24 P Erdös (1569_CR24) 1946; 52 |
| References_xml | – volume: 20 start-page: 255 year: 2003 end-page: 264 ident: CR40 article-title: Orderings on graphs and game coloring number publication-title: Order doi: 10.1023/B:ORDE.0000026489.93166.cb contributor: fullname: Yang – ident: CR45 – ident: CR22 – volume: 55 start-page: 1 issue: 3 year: 2008 end-page: 53 ident: CR59 article-title: Homomorphism preservation theorems publication-title: J. ACM doi: 10.1145/1379759.1379763 contributor: fullname: Rossman – volume: 29 start-page: 3 year: 1976 end-page: 10 ident: CR64 article-title: Coloring the vertices of a graph in prescribed colors publication-title: Metody Diskretnogo Analiza v Teorii Kodov i Schem contributor: fullname: Vizing – ident: CR39 – volume: 62 start-page: 11 issue: 1 year: 1994 end-page: 33 ident: CR63 article-title: Five-coloring graphs on the torus publication-title: J. Combin. Theory Ser. B doi: 10.1006/jctb.1994.1052 contributor: fullname: Thomassen – ident: CR12 – volume: 91 start-page: 25 year: 2004 end-page: 41 ident: CR13 article-title: Excluding any graph as a minor allows a low tree-width 2-coloring publication-title: J. Combin. Theory Ser. B doi: 10.1016/j.jctb.2003.09.001 contributor: fullname: Vertigan – volume: 27 start-page: 1022 issue: 6 year: 2006 end-page: 1041 ident: CR47 article-title: Tree depth, subgraph coloring and homomorphism bounds publication-title: Eur. J. Combin. doi: 10.1016/j.ejc.2005.01.010 contributor: fullname: Ossona de Mendez – ident: CR29 – ident: CR54 – ident: CR61 – ident: CR58 – volume: 85 start-page: 12 year: 1990 end-page: 75 ident: CR10 article-title: The monadic second-order logic of graphs I: recognizable sets of finite graphs publication-title: Inform. Comput. doi: 10.1016/0890-5401(90)90043-H contributor: fullname: Courcelle – volume: 130 start-page: 3 issue: 1–3 year: 2004 end-page: 31 ident: CR26 article-title: The complexity of first-order and monadic second-order logic revisited publication-title: Ann. Pure Appl. Logic doi: 10.1016/j.apal.2004.01.007 contributor: fullname: Grohe – ident: CR42 – volume: 29 start-page: 777 issue: 3 year: 2008 end-page: 791 ident: CR49 article-title: Grad and classes with bounded expansion II. Algorithmic aspects publication-title: Eur. J. Combin. doi: 10.1016/j.ejc.2006.07.014 contributor: fullname: Ossona de Mendez – volume: 309 start-page: 5789 issue: 18 year: 2009 end-page: 5798 ident: CR44 article-title: Homomorphisms of triangle-free graphs without a -minor publication-title: Discrete Math. doi: 10.1016/j.disc.2009.04.032 contributor: fullname: Škrekovski – ident: CR46 – volume: 32 start-page: 600 issue: 4 year: 2011 end-page: 617 ident: CR52 article-title: On nowhere dense graphs publication-title: Eur. J. Combin. doi: 10.1016/j.ejc.2011.01.006 contributor: fullname: Ossona de Mendez – volume: 33 start-page: 969 issue: 5 year: 2012 end-page: 979 ident: CR16 article-title: Forbidden graphs for tree-depth publication-title: Eur. J. Combin. doi: 10.1016/j.ejc.2011.09.014 contributor: fullname: Thilikos – ident: CR19 – volume: 159 start-page: 2045 year: 2011 end-page: 2049 ident: CR25 article-title: Thue choosability of trees publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2011.07.017 contributor: fullname: Zhu – volume: 29 start-page: 1012 issue: 4 year: 2008 end-page: 1024 ident: CR50 article-title: Grad and classes with bounded expansion III. Restricted graph homomorphism dualities publication-title: Eur. J. Combin. doi: 10.1016/j.ejc.2007.11.019 contributor: fullname: Ossona de Mendez – ident: CR15 – ident: CR11 – volume: 10 start-page: 385 issue: 4 year: 1963 end-page: 397 ident: CR18 article-title: Transition graphs and the star-height of regular events publication-title: Mich. Math. J. doi: 10.1307/mmj/1028998975 contributor: fullname: Eggan – ident: CR57 – ident: CR32 – volume: 16 start-page: 489 issue: 5 year: 1992 end-page: 502 ident: CR14 article-title: Subgraphs and well-quasi-ordering publication-title: J. Graph Theory doi: 10.1002/jgt.3190160509 contributor: fullname: Ding – ident: CR36 – volume: 42 start-page: 844 issue: 4 year: 1995 end-page: 856 ident: CR4 article-title: Color-coding publication-title: J. ACM doi: 10.1145/210332.210337 contributor: fullname: Zwick – ident: CR5 – volume: 24 start-page: 155 issue: 1 year: 2004 end-page: 162 ident: CR41 article-title: Every graph of sufficiently large average degree contains a -free subgraph of large average degree publication-title: Combinatorica doi: 10.1007/s00493-004-0010-2 contributor: fullname: Osthus – volume: 24 start-page: 105 issue: 1 year: 1978 end-page: 107 ident: CR31 article-title: Trivially perfect graphs publication-title: Discrete Math. doi: 10.1016/0012-365X(78)90178-4 contributor: fullname: Golumbic – year: 2004 ident: CR35 publication-title: Graphs and Homomorphisms, Oxford Lecture Series in Mathematics and its Applications doi: 10.1093/acprof:oso/9780198528173.001.0001 contributor: fullname: Nešetřil – volume: 97 start-page: 394 issue: 3 year: 2007 end-page: 400 ident: CR43 article-title: Homomorphisms and edge-coloring of planar graphs publication-title: J. Combin. Theory Ser. B doi: 10.1016/j.jctb.2006.07.001 contributor: fullname: Naserasr – volume: 32 start-page: 1126 issue: 7 year: 2011 end-page: 1141 ident: CR51 article-title: How many F’s are there in G? publication-title: Eur. J. Combin. doi: 10.1016/j.ejc.2011.03.007 contributor: fullname: Ossona de Mendez – volume: 309 start-page: 5562 issue: 18 year: 2009 end-page: 5568 ident: CR66 article-title: Colouring graphs with bounded generalized colouring number publication-title: Discrete Math. doi: 10.1016/j.disc.2008.03.024 contributor: fullname: Zhu – volume: 58 start-page: 22 year: 1993 end-page: 33 ident: CR62 article-title: Graph searching and a min–max theorem for tree-width publication-title: J. Combin. Theory Ser. B doi: 10.1006/jctb.1993.1027 contributor: fullname: Thomas – volume: 29 start-page: 760 issue: 3 year: 2008 end-page: 776 ident: CR48 article-title: Grad and classes with bounded expansion I. Decompositions publication-title: Eur. J. Combin. doi: 10.1016/j.ejc.2006.07.013 contributor: fullname: Ossona de Mendez – ident: CR53 – volume: 9 start-page: 251 year: 1990 end-page: 280 ident: CR9 article-title: Matrix multiplication via arithmetic progressions publication-title: J. Symbolic Comput. doi: 10.1016/S0747-7171(08)80013-2 contributor: fullname: Winograd – volume: 24 start-page: 649 issue: 6 year: 2003 end-page: 663 ident: CR56 article-title: On the order of countable graphs publication-title: Eur. J. Combin. doi: 10.1016/S0195-6698(03)00064-7 contributor: fullname: Shelah – ident: CR33 – ident: CR6 – volume: 25 start-page: 211 issue: 3 year: 1979 end-page: 236 ident: CR7 article-title: On acyclic colorings of planar graphs publication-title: Discrete Math. doi: 10.1016/0012-365X(79)90077-3 contributor: fullname: Borodin – volume: 12 start-page: 477 issue: 5+ 6 year: 2003 end-page: 494 ident: CR1 article-title: Turán numbers of bipartite graphs and related ramsey-type questions publication-title: Comb. Probab. Comput. doi: 10.1017/S0963548303005741 contributor: fullname: Sudakov – volume: 3 start-page: 1 issue: 3 year: 1999 end-page: 27 ident: CR21 article-title: Subgraph isomorphism in planar graphs and related problems publication-title: J. Graph Algorithms Appl. doi: 10.7155/jgaa.00014 contributor: fullname: Eppstein – ident: CR27 – volume: 86 start-page: 243 year: 1991 end-page: 266 ident: CR8 article-title: Planar orientations with low out-degree and compaction of adjacency matrices publication-title: Theor. Comput. Sci. doi: 10.1016/0304-3975(91)90020-3 contributor: fullname: Eppstein – ident: CR23 – year: 2011 ident: CR37 publication-title: Graph Coloring Problems contributor: fullname: Toft – volume: 26 start-page: 415 issue: 2 year: 1985 end-page: 420 ident: CR55 article-title: Complexity of the subgraph problem publication-title: Comment Math. Univ. Carol. contributor: fullname: Poljak – ident: CR65 – ident: CR38 – volume: 94 start-page: 273 year: 1994 end-page: 283 ident: CR3 article-title: On acyclic colorings of graphs on surfaces publication-title: Israel J. Math. doi: 10.1007/BF02762708 contributor: fullname: Sanders – ident: CR17 – ident: CR34 – ident: CR28 – volume: 52 start-page: 1087 year: 1946 end-page: 1091 ident: CR24 article-title: On the structure of linear graphs publication-title: Bull. Am. Math. Soc doi: 10.1090/S0002-9904-1946-08715-7 contributor: fullname: Stone – volume: 6 start-page: 2 issue: 3 year: 1977 ident: CR60 article-title: -colorings of planar graphs publication-title: Graph Theory Newslett. contributor: fullname: Sampathkumar – volume: 12 start-page: 375 year: 1992 end-page: 380 ident: CR2 article-title: Star arboricity publication-title: Combinatorica doi: 10.1007/BF01305230 contributor: fullname: Reed – ident: CR20 – volume: 160 start-page: 2089 issue: 15 year: 2012 end-page: 2097 ident: CR30 article-title: LIFO-search: a minmax theorem and a searching game for cycle-rank and tree-depth publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2012.03.015 contributor: fullname: Thilikos – ident: 1569_CR53 doi: 10.1007/978-3-642-27875-4 – volume: 32 start-page: 600 issue: 4 year: 2011 ident: 1569_CR52 publication-title: Eur. J. Combin. doi: 10.1016/j.ejc.2011.01.006 contributor: fullname: J Nešetřil – volume: 52 start-page: 1087 year: 1946 ident: 1569_CR24 publication-title: Bull. Am. Math. Soc doi: 10.1090/S0002-9904-1946-08715-7 contributor: fullname: P Erdös – ident: 1569_CR65 – ident: 1569_CR36 doi: 10.1007/978-3-642-22953-4_19 – volume: 16 start-page: 489 issue: 5 year: 1992 ident: 1569_CR14 publication-title: J. Graph Theory doi: 10.1002/jgt.3190160509 contributor: fullname: G Ding – ident: 1569_CR42 doi: 10.1007/978-3-642-39206-1_57 – volume-title: Graph Coloring Problems year: 2011 ident: 1569_CR37 contributor: fullname: T Jensen – volume: 62 start-page: 11 issue: 1 year: 1994 ident: 1569_CR63 publication-title: J. Combin. Theory Ser. B doi: 10.1006/jctb.1994.1052 contributor: fullname: C Thomassen – ident: 1569_CR27 – volume: 12 start-page: 375 year: 1992 ident: 1569_CR2 publication-title: Combinatorica doi: 10.1007/BF01305230 contributor: fullname: N Alon – ident: 1569_CR46 doi: 10.1145/1132516.1132575 – volume: 12 start-page: 477 issue: 5+ 6 year: 2003 ident: 1569_CR1 publication-title: Comb. Probab. Comput. doi: 10.1017/S0963548303005741 contributor: fullname: N Alon – ident: 1569_CR23 – volume: 309 start-page: 5789 issue: 18 year: 2009 ident: 1569_CR44 publication-title: Discrete Math. doi: 10.1016/j.disc.2009.04.032 contributor: fullname: R Naserasr – ident: 1569_CR28 doi: 10.2168/LMCS-11(1:19)2015 – volume: 27 start-page: 1022 issue: 6 year: 2006 ident: 1569_CR47 publication-title: Eur. J. Combin. doi: 10.1016/j.ejc.2005.01.010 contributor: fullname: J Nešetřil – ident: 1569_CR5 – volume: 85 start-page: 12 year: 1990 ident: 1569_CR10 publication-title: Inform. Comput. doi: 10.1016/0890-5401(90)90043-H contributor: fullname: B Courcelle – volume: 32 start-page: 1126 issue: 7 year: 2011 ident: 1569_CR51 publication-title: Eur. J. Combin. doi: 10.1016/j.ejc.2011.03.007 contributor: fullname: J Nešetřil – volume: 97 start-page: 394 issue: 3 year: 2007 ident: 1569_CR43 publication-title: J. Combin. Theory Ser. B doi: 10.1016/j.jctb.2006.07.001 contributor: fullname: R Naserasr – volume: 24 start-page: 649 issue: 6 year: 2003 ident: 1569_CR56 publication-title: Eur. J. Combin. doi: 10.1016/S0195-6698(03)00064-7 contributor: fullname: J Nešetřil – ident: 1569_CR34 doi: 10.1007/978-3-642-03816-7_33 – volume: 42 start-page: 844 issue: 4 year: 1995 ident: 1569_CR4 publication-title: J. ACM doi: 10.1145/210332.210337 contributor: fullname: N Alon – ident: 1569_CR6 doi: 10.1007/3-540-59071-4 – volume: 58 start-page: 22 year: 1993 ident: 1569_CR62 publication-title: J. Combin. Theory Ser. B doi: 10.1006/jctb.1993.1027 contributor: fullname: P Seymour – ident: 1569_CR32 doi: 10.1145/2591796.2591851 – volume: 159 start-page: 2045 year: 2011 ident: 1569_CR25 publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2011.07.017 contributor: fullname: F Fiorenzi – volume-title: Graphs and Homomorphisms, Oxford Lecture Series in Mathematics and its Applications year: 2004 ident: 1569_CR35 doi: 10.1093/acprof:oso/9780198528173.001.0001 contributor: fullname: P Hell – ident: 1569_CR20 – ident: 1569_CR12 doi: 10.1007/3-540-57785-8_187 – ident: 1569_CR29 doi: 10.1007/978-3-642-32589-2_38 – ident: 1569_CR54 doi: 10.1007/978-88-7642-525-7_6 – ident: 1569_CR15 – volume: 33 start-page: 969 issue: 5 year: 2012 ident: 1569_CR16 publication-title: Eur. J. Combin. doi: 10.1016/j.ejc.2011.09.014 contributor: fullname: Z Dvořák – volume: 24 start-page: 105 issue: 1 year: 1978 ident: 1569_CR31 publication-title: Discrete Math. doi: 10.1016/0012-365X(78)90178-4 contributor: fullname: M Golumbic – volume: 20 start-page: 255 year: 2003 ident: 1569_CR40 publication-title: Order doi: 10.1023/B:ORDE.0000026489.93166.cb contributor: fullname: H Kierstead – volume: 29 start-page: 1012 issue: 4 year: 2008 ident: 1569_CR50 publication-title: Eur. J. Combin. doi: 10.1016/j.ejc.2007.11.019 contributor: fullname: J Nešetřil – ident: 1569_CR57 doi: 10.1007/3-540-53832-1_28 – volume: 6 start-page: 2 issue: 3 year: 1977 ident: 1569_CR60 publication-title: Graph Theory Newslett. contributor: fullname: E Sampathkumar – ident: 1569_CR11 – volume: 91 start-page: 25 year: 2004 ident: 1569_CR13 publication-title: J. Combin. Theory Ser. B doi: 10.1016/j.jctb.2003.09.001 contributor: fullname: M DeVos – volume: 55 start-page: 1 issue: 3 year: 2008 ident: 1569_CR59 publication-title: J. ACM doi: 10.1145/1379759.1379763 contributor: fullname: B Rossman – volume: 160 start-page: 2089 issue: 15 year: 2012 ident: 1569_CR30 publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2012.03.015 contributor: fullname: A Giannopoulou – ident: 1569_CR33 doi: 10.1007/978-3-540-70583-3_4 – volume: 26 start-page: 415 issue: 2 year: 1985 ident: 1569_CR55 publication-title: Comment Math. Univ. Carol. contributor: fullname: J Nešetřil – volume: 25 start-page: 211 issue: 3 year: 1979 ident: 1569_CR7 publication-title: Discrete Math. doi: 10.1016/0012-365X(79)90077-3 contributor: fullname: O Borodin – ident: 1569_CR58 – ident: 1569_CR17 doi: 10.1145/2499483 – volume: 24 start-page: 155 issue: 1 year: 2004 ident: 1569_CR41 publication-title: Combinatorica doi: 10.1007/s00493-004-0010-2 contributor: fullname: D Kühn – volume: 309 start-page: 5562 issue: 18 year: 2009 ident: 1569_CR66 publication-title: Discrete Math. doi: 10.1016/j.disc.2008.03.024 contributor: fullname: X Zhu – ident: 1569_CR39 doi: 10.1145/2463664.2463667 – ident: 1569_CR61 doi: 10.1016/0020-0190(89)90161-0 – volume: 3 start-page: 1 issue: 3 year: 1999 ident: 1569_CR21 publication-title: J. Graph Algorithms Appl. doi: 10.7155/jgaa.00014 contributor: fullname: D Eppstein – volume: 130 start-page: 3 issue: 1–3 year: 2004 ident: 1569_CR26 publication-title: Ann. Pure Appl. Logic doi: 10.1016/j.apal.2004.01.007 contributor: fullname: M Frick – volume: 29 start-page: 3 year: 1976 ident: 1569_CR64 publication-title: Metody Diskretnogo Analiza v Teorii Kodov i Schem contributor: fullname: V Vizing – ident: 1569_CR19 doi: 10.1109/LICS.2012.37 – volume: 29 start-page: 777 issue: 3 year: 2008 ident: 1569_CR49 publication-title: Eur. J. Combin. doi: 10.1016/j.ejc.2006.07.014 contributor: fullname: J Nešetřil – volume: 10 start-page: 385 issue: 4 year: 1963 ident: 1569_CR18 publication-title: Mich. Math. J. doi: 10.1307/mmj/1028998975 contributor: fullname: L Eggan – volume: 9 start-page: 251 year: 1990 ident: 1569_CR9 publication-title: J. Symbolic Comput. doi: 10.1016/S0747-7171(08)80013-2 contributor: fullname: D Coppersmith – ident: 1569_CR22 doi: 10.1007/s004530010020 – ident: 1569_CR38 doi: 10.1002/jgt.20522 – volume: 94 start-page: 273 year: 1994 ident: 1569_CR3 publication-title: Israel J. Math. doi: 10.1007/BF02762708 contributor: fullname: N Alon – volume: 86 start-page: 243 year: 1991 ident: 1569_CR8 publication-title: Theor. Comput. Sci. doi: 10.1016/0304-3975(91)90020-3 contributor: fullname: M Chrobak – ident: 1569_CR45 doi: 10.1007/978-3-642-55566-4_29 – volume: 29 start-page: 760 issue: 3 year: 2008 ident: 1569_CR48 publication-title: Eur. J. Combin. doi: 10.1016/j.ejc.2006.07.013 contributor: fullname: J Nešetřil |
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