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Chi-boundedness of graph classes excluding wheel vertex-minorsopen access
- Authors
- Choi, Hojin; Kwon, O-joung; Oum, Sang-il; Wollan, Paul
- Issue Date
- Mar-2019
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Chromatic number; chi-bounded class; Vertex-minor; Wheel graph
- Citation
- JOURNAL OF COMBINATORIAL THEORY SERIES B, v.135, pp.319 - 348
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF COMBINATORIAL THEORY SERIES B
- Volume
- 135
- Start Page
- 319
- End Page
- 348
- ISSN
- 0095-8956
- Abstract
- A class of graphs is X-bounded if there exists a function f : N -> Nsuch that for every graph G in the class and an induced subgraph H of G, if H has no clique of size q + 1, then the chromatic number of H is less than or equal to f(q). We denote by W-n the wheel graph on n +1 vertices. We show that the class of graphs having no vertex-minor isomorphic to W-n is chi-bounded. This generalizes several previous results; chi-boundedness for circle graphs, for graphs having no W-5 vertex-minors, and for graphs having no fan vertex-minors.
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Related Researcher
- Kwon, O jung
- COLLEGE OF NATURAL SCIENCES (DEPARTMENT OF MATHEMATICS)