MANIFOLD MATCHING COMPLEXES
The matching complex of a graph is the simplicial complex whose vertex set is the set of edges of the graph with a face for each independent set of edges. In this paper, we completely characterize the pairs (graph, matching complex) for which the matching complex is a homology manifold, with or with...
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| Published in: | Mathematika Vol. 66; no. 4; pp. 973 - 1002 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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01-10-2020
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| Abstract | The matching complex of a graph is the simplicial complex whose vertex set is the set of edges of the graph with a face for each independent set of edges. In this paper, we completely characterize the pairs (graph, matching complex) for which the matching complex is a homology manifold, with or without boundary. Except in dimension two, all of these manifolds are spheres or balls. |
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| AbstractList | The matching complex of a graph is the simplicial complex whose vertex set is the set of edges of the graph with a face for each independent set of edges. In this paper, we completely characterize the pairs (graph, matching complex) for which the matching complex is a homology manifold, with or without boundary. Except in dimension two, all of these manifolds are spheres or balls. |
| Author | Bayer, Margaret Goeckner, Bennet Jelić Milutinović, Marija |
| Author_xml | – sequence: 1 givenname: Margaret surname: Bayer fullname: Bayer, Margaret email: bayer@ku.edu organization: University of Kansas – sequence: 2 givenname: Bennet surname: Goeckner fullname: Goeckner, Bennet email: goeckner@uw.edu organization: University of Washington – sequence: 3 givenname: Marija surname: Jelić Milutinović fullname: Jelić Milutinović, Marija email: marijaj@matf.bg.ac.rs organization: University of Belgrade |
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| Cites_doi | 10.1090/S0002-9947-1964-0158382-7 10.1007/BF02772986 10.1007/978-1-4613-0019-9 10.1007/s11856-008-0024-3 10.1016/j.aim.2006.10.014 10.1007/s00012-003-1825-1 10.1007/978-3-540-75859-4 10.37236/8480 10.1112/jlms/49.1.25 10.37236/825 10.1007/s00454-003-2869-x 10.1007/978-3-319-24298-9_26 10.37236/6212 10.1006/jcta.1999.2984 |
| ContentType | Journal Article |
| Copyright | 2020 The Authors. The publishing rights for this article are licensed to University College London under an exclusive licence. |
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| GrantInformation_xml | – fundername: Simons Foundation funderid: #316262; #426971 – fundername: NSF funderid: 1603823; 1604773; 1604458 – fundername: Ministry of Education, Science and Technological Development funderid: #174034 – fundername: NSA funderid: H98230‐18‐1‐0017 |
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| Notes | This work was done in part at the 2018 Graduate Research Workshop in Combinatorics. The workshop was partially funded by NSF grants 1603823, 1604773, and 1604458, “Collaborative Research: Rocky Mountain ‐ Great Plains Graduate Research Workshops in Combinatorics,” NSA grant H98230‐18‐1‐0017, “The 2018 and 2019 Rocky Mountain ‐ Great Plains Graduate Research Workshops in Combinatorics,” Simons Foundation Collaboration Grants #316262 and #426971, and grants from the Combinatorics Foundation and the Institute for Mathematics and its Applications. Margaret Bayer also received support from the University of Kansas General Research Fund. Bennet Goeckner also received support from an AMS‐Simons travel grant. Marija Jelić Milutinović also received support from Grant #174034 of the Ministry of Education, Science and Technological Development of Serbia. |
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| References | 2004; 31 2018; 8 2007; 212 2010; 46 2017; 24 2019; 26 2019 2008 1964; 111 2008; 15 2018 1999; 88 1996 2003; 49 1994; 49 2016 2003 2008; 164 1994; 87 e_1_2_9_11_1 Klee S. (e_1_2_9_13_1) 2016 e_1_2_9_21_1 e_1_2_9_12_1 Kwun K. W. (e_1_2_9_15_1) 1964; 111 e_1_2_9_8_1 Matsushita T. (e_1_2_9_17_1) 2019; 26 Jojić D. (e_1_2_9_10_1) 2018; 8 e_1_2_9_5_1 e_1_2_9_3_1 Braun B. (e_1_2_9_4_1) 2017; 24 Athanasiadis C. A. (e_1_2_9_2_1) 2004; 31 Frohmader A. (e_1_2_9_7_1) 2008; 164 Marietti M. (e_1_2_9_16_1) 2008; 15 Stanley R. P. (e_1_2_9_19_1) 1996 e_1_2_9_9_1 Frendrup A. (e_1_2_9_6_1) 2010; 46 Wachs M. L. (e_1_2_9_20_1) 2003; 49 Kozlov D. N. (e_1_2_9_14_1) 1999; 88 e_1_2_9_18_1 |
| References_xml | – volume: 49 start-page: 25 issue: 1 year: 1994 end-page: 39 article-title: Chessboard complexes and matching complexes publication-title: J. Lond. Math. Soc. (2) – volume: 87 start-page: 97 issue: 1–3 year: 1994 end-page: 110 article-title: Shellability of chessboard complexes publication-title: Israel J. Math. – volume: 111 start-page: 108 year: 1964 end-page: 120 article-title: Manifolds which are joins publication-title: Trans. Amer. Math. Soc. – volume: 88 start-page: 112 issue: 1 year: 1999 end-page: 122 article-title: Complexes of directed trees publication-title: J. Combin. Theory Ser. A – volume: 24 issue: 4 year: 2017 article-title: Matching and independence complexes related to small grids publication-title: Electron. J. Combin. – volume: 8 start-page: 413 issue: 3 year: 2018 end-page: 421 article-title: On the ‐vectors of chessboard complexes publication-title: Bull. Int. Math. Virtual Inst. – year: 2008 – year: 2003 – volume: 31 start-page: 395 issue: 3 year: 2004 end-page: 403 article-title: Decompositions and connectivity of matching and chessboard complexes publication-title: Discrete Comput. Geom. – volume: 15 issue: 1 year: 2008 article-title: A uniform approach to complexes arising from forests publication-title: Electron. J. Combin. – year: 1996 – start-page: 653 year: 2016 end-page: 686 – volume: 49 start-page: 345 issue: 4 year: 2003 end-page: 385 article-title: Topology of matching, chessboard, and general bounded degree graph complexes publication-title: Algebra Universalis – volume: 212 start-page: 525 issue: 2 year: 2007 end-page: 570 article-title: Torsion in the matching complex and chessboard complex publication-title: Adv. Math. – year: 2018 – year: 2019 – volume: 46 start-page: 185 year: 2010 end-page: 190 article-title: A note on equimatchable graphs publication-title: Australas. J. Combin. – volume: 164 start-page: 153 year: 2008 end-page: 164 article-title: Face vectors of flag complexes publication-title: Israel J. Math. – volume: 26 issue: 3 year: 2019 article-title: Matching complexes of small grids publication-title: Electron. J. Combin. – volume: 111 start-page: 108 year: 1964 ident: e_1_2_9_15_1 article-title: Manifolds which are joins publication-title: Trans. Amer. Math. Soc. doi: 10.1090/S0002-9947-1964-0158382-7 contributor: fullname: Kwun K. W. – ident: e_1_2_9_21_1 doi: 10.1007/BF02772986 – ident: e_1_2_9_5_1 – ident: e_1_2_9_8_1 doi: 10.1007/978-1-4613-0019-9 – volume: 164 start-page: 153 year: 2008 ident: e_1_2_9_7_1 article-title: Face vectors of flag complexes publication-title: Israel J. Math. doi: 10.1007/s11856-008-0024-3 contributor: fullname: Frohmader A. – ident: e_1_2_9_18_1 doi: 10.1016/j.aim.2006.10.014 – volume: 49 start-page: 345 issue: 4 year: 2003 ident: e_1_2_9_20_1 article-title: Topology of matching, chessboard, and general bounded degree graph complexes publication-title: Algebra Universalis doi: 10.1007/s00012-003-1825-1 contributor: fullname: Wachs M. L. – ident: e_1_2_9_11_1 doi: 10.1007/978-3-540-75859-4 – volume: 26 issue: 3 year: 2019 ident: e_1_2_9_17_1 article-title: Matching complexes of small grids publication-title: Electron. J. Combin. doi: 10.37236/8480 contributor: fullname: Matsushita T. – ident: e_1_2_9_3_1 doi: 10.1112/jlms/49.1.25 – ident: e_1_2_9_12_1 – volume: 15 issue: 1 year: 2008 ident: e_1_2_9_16_1 article-title: A uniform approach to complexes arising from forests publication-title: Electron. J. Combin. doi: 10.37236/825 contributor: fullname: Marietti M. – volume: 31 start-page: 395 issue: 3 year: 2004 ident: e_1_2_9_2_1 article-title: Decompositions and connectivity of matching and chessboard complexes publication-title: Discrete Comput. Geom. doi: 10.1007/s00454-003-2869-x contributor: fullname: Athanasiadis C. A. – volume-title: Combinatorics and Commutative Algebra year: 1996 ident: e_1_2_9_19_1 contributor: fullname: Stanley R. P. – start-page: 653 volume-title: Recent Trends in Combinatorics year: 2016 ident: e_1_2_9_13_1 doi: 10.1007/978-3-319-24298-9_26 contributor: fullname: Klee S. – volume: 46 start-page: 185 year: 2010 ident: e_1_2_9_6_1 article-title: A note on equimatchable graphs publication-title: Australas. J. Combin. contributor: fullname: Frendrup A. – volume: 24 issue: 4 year: 2017 ident: e_1_2_9_4_1 article-title: Matching and independence complexes related to small grids publication-title: Electron. J. Combin. doi: 10.37236/6212 contributor: fullname: Braun B. – ident: e_1_2_9_9_1 – volume: 8 start-page: 413 issue: 3 year: 2018 ident: e_1_2_9_10_1 article-title: On the h‐vectors of chessboard complexes publication-title: Bull. Int. Math. Virtual Inst. contributor: fullname: Jojić D. – volume: 88 start-page: 112 issue: 1 year: 1999 ident: e_1_2_9_14_1 article-title: Complexes of directed trees publication-title: J. Combin. Theory Ser. A doi: 10.1006/jcta.1999.2984 contributor: fullname: Kozlov D. N. |
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| Title | MANIFOLD MATCHING COMPLEXES |
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