Geelen's chi-boundedness conjecture for graphs excluding a vertex-minor
Geelen's chi-boundedness conjecture for graphs excluding a vertex-minor
Let be a graph. A class of graphs is -bounded if there exists a function such that for every graph in the class and every induced subgraph of , , where and denote the chromatic and clique numbers of , respectively. A vertex-minor of a graph is an induced subgraph of a graph obtained by a sequence of local complementations. Geelen's conjecture. For every graph , the class of graphs with no vertex-minor is -bounded. This conjecture extends known -boundedness results for circle graphs and graphs of bounded rank-width; its general case remains open.
Sources & referencesView supporting material
Primary source
Hojin Choi, O-joung Kwon, Sang-il Oum and Paul Wollan, “Chi-boundedness of graph classes excluding wheel vertex-minors”, arXiv:1702.07851 (2018).
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