Elsevier

Discrete Mathematics

Volume 313, Issue 4, 28 February 2013, Pages 366-374
Discrete Mathematics

On almost (k1)-degenerate (k+1)-chromatic graphs and hypergraphs

https://doi.org/10.1016/j.disc.2012.11.010Get rights and content
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Abstract

Recall that a (hyper)graph is d-degenerate if each of its nonempty subgraphs has a vertex of degree at most d. Every d-degenerate (hyper)graph is (easily) (d+1)-colorable. A (hyper)graph is almost d-degenerate if it is not d-degenerate, but each of its proper subgraphs is d-degenerate. In particular, if G is almost (k1)-degenerate, then after deleting any edge it is k-colorable. For k2, we study properties of almost (k1)-degenerate (hyper)graphs that are not k-colorable. By definition, each such (hyper)graph is (k+1)-critical.

Keywords

Color critical graph
k-degenerate graph

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