Defective Colouring of Graphs Excluding A Subgraph or Minor

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Archdeacon (1987) proved that graphs embeddable on a fixed surface can be 3-coloured so that each colour class induces a subgraph of bounded maximum degree. Edwards, Kang, Kim, Oum and Seymour (2015) proved that graphs with no Kt+1-minor can be t-coloured so that each colour class induces a subgraph of bounded maximum degree. We prove a common generalisation of these theorems with a weaker assumption about excluded subgraphs. This result leads to new defective colouring results for several graph classes, including graphs with linear crossing number, graphs with given thickness (with relevance to the earth-moon problem), graphs with given stack- or queue-number, linklessly or knotlessly embeddable graphs, graphs with given Colin de Verdiere parameter, and graphs excluding a complete bipartite graph as a topological minor.
Publisher
SPRINGER HEIDELBERG
Issue Date
2019-04
Language
English
Article Type
Article
Citation

COMBINATORICA, v.39, no.2, pp.377 - 410

ISSN
0209-9683
DOI
10.1007/s00493-018-3733-1
URI
http://hdl.handle.net/10203/263207
Appears in Collection
MA-Journal Papers(저널논문)
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