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On the genus of graphs with Lick-White number $ k$

Author: John Mitchem
Journal: Proc. Amer. Math. Soc. 69 (1978), 349-354
MSC: Primary 05C15; Secondary 05C10
MathSciNet review: 0476560
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Abstract: A graph is called n-degenerate if each of its subgraphs has a vertex of degree at most n. For each n the Lick-White number of graph G is the fewest number of sets into which $ V(G)$ can be partitioned such that each set induces an n-degenerate graph. An upper bound is obtained for the Lick-White number of graphs with given clique number. A number of estimates are derived for the number of vertices in triangle-free graphs with prescribed Lick-White number. These results are used to give lower bounds on the genus of such graphs.

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Keywords: n-degenerate graph, Lick-White number, genus
Article copyright: © Copyright 1978 American Mathematical Society