Search Results - "Mark, Siggers"

The Complexity of the Matroid Homomorphism Problem by Heo, Cheolwon, Kim, Hyobin, Mark, Siggers

“…We show that for every binary matroid $N$ there is a graph $H_*$ such that for the graphic matroid $M_G$ of a graph $G$, there is a matroid-homomorphism from…”
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Dichotomy for bounded degree H -colouring by Siggers, Mark H.

“…Given a graph H , let b ( H ) be the minimum integer b , if it exists, for which H -colouring is N P -complete when restricted to instances with degree bounded…”
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The maximum size of intersecting and union families of sets by Siggers, Mark, Tokushige, Norihide

“…We consider the maximal size of families of k -element subsets of an n element set [ n ] that satisfy the properties that every r subsets of the family have…”
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A reflexive digraph that is retraction trivial but not endomorphism trivial by Siggers, Mark

“…In this note we give an example of a reflexive digraph that has no non-trivial retractions, but does have non-trivial endomorphisms…”
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Reflexive Graphs with Near Unanimity but no Semilattice Polymorphisms by Siggers, Mark

“…We show that every generator, in a certain set of generators for the variety of reflexive near unanimity graphs, admits a semilattice polymorphism. We then…”
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Non-bipartite pairs of 3-connected graphs are highly Ramsey-infinite by Siggers, Mark

“…A pair of graphs (Hb,Hr) is highly Ramsey-infinite if there is some constant c such that for large enough n there are at least 2cn2 non-isomorphic graphs on n…”
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Mixing is hard for triangle-free reflexive graphs by Kim, Hyobeen, Lee, Jae-baek, Siggers, Mark

“…In the problem Mix(H) one is given a graph G and must decide if the Hom-graph Hom(G,H) is connected. We show that if H is a triangle-free reflexive graph with…”
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A strong Mal’cev condition for locally finite varieties omitting the unary type by Siggers, Mark H.

“…We show that a finite algebra has a Taylor operation if and only if it has an operation satisfying a particular set of 6-ary Taylor identities. As a…”
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Non-bipartite pairs of 33-connected graphs are highly Ramsey-infinite by Siggers, Mark

“…A pair of graphs (Hb,Hr) is highly Ramsey-infinite if there is some constant cc such that for large enough nn there are at least 2cn22cn2 non-isomorphic graphs…”
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Locally injective k-colourings of planar graphs by Kratochvil, Jan, Siggers, Mark

“…A colouring of the vertices of a graph is called injective if every two distinct vertices connected by a path of length 2 receive different colours, and it is…”
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Locally injective kk-colourings of planar graphs by Kratochvil, Jan, Siggers, Mark

“…A colouring of the vertices of a graph is called injective if every two distinct vertices connected by a path of length 2 receive different colours, and it is…”
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Towards extending the Ahlswede–Khachatrian theorem to cross t-intersecting families by Lee, Sang June, Siggers, Mark, Tokushige, Norihide

“…Ahlswede and Khachatrian’s diametric theorem is a weighted version of their complete intersection theorem, which is itself a well known extension of the…”
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Corrigendum to “Reconfiguring graph homomorphisms on the sphere” [European J. Combin. 86 (2020) 103086] by Lee, Jae-Baek, Noel, Jonathan A., Siggers, Mark

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Decompositions of graphs into trees, forests, and regular subgraphs by Akbari, Saieed, Jensen, Tommy R., Siggers, Mark

“…A conjecture by A. Hoffmann-Ostenhof suggests that any connected cubic graph G contains a spanning tree T for which every component of G−E(T) is a K1, a K2, or…”
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Reconfiguration of homomorphisms to reflexive digraph cycles by Brewster, Richard C., Lee, Jae-baek, Siggers, Mark

“…Let G be a digraph and B be a fixed reflexive digraph cycle. Given two homomorphisms ϕ,ϕ′:G→B, a walk from ϕ to ϕ′ in the Hom-graph Hom(G,B) corresponds to…”
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Recolouring homomorphisms to triangle-free reflexive graphs by Lee, Jae baek, Noel, Jonathan A., Siggers, Mark

“…For a graph H , the H -recolouring problem Recol ( H ) asks, for two given homomorphisms from a given graph G to H , if one can get between them by a sequence…”
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Semilattice polymorphisms and chordal graphs by Hell, Pavol, Siggers, Mark

“…We investigate the class of reflexive graphs that admit semilattice polymorphisms, and in doing so, give an algebraic characterisation of chordal graphs. In…”
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Characterisation of forests with trivial game domination numbers by Nadjafi-Arani, M. J., Siggers, Mark, Soltani, Hossein

“…In the domination game, two players, the Dominator and Staller, take turns adding vertices of a fixed graph to a set, at each turn increasing the number of…”
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An Erdős–Ko–Rado theorem for cross t-intersecting families by Frankl, Peter, Lee, Sang June, Siggers, Mark, Tokushige, Norihide

“…Two families A and B, of k-subsets of an n-set, are cross t-intersecting if for every choice of subsets A∈A and B∈B we have |A∩B|≥t. We address the following…”
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A Brightwell-Winkler type characterisation of NU graphs by Siggers, Mark

“…In 2000, Brightwell and Winkler characterised dismantlable graphs as the graphs $H$ for which the Hom-graph ${\rm Hom}(G,H)$, defined on the set of…”
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