The Hadwiger number, chordal graphs and ab -perfection

Citation data:

AKCE International Journal of Graphs and Combinatorics, ISSN: 0972-8600, Vol: 14, Issue: 2, Page: 130-134

Publication Year:
2017
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DOI:
10.1016/j.akcej.2017.02.004
Author(s):
Christian Rubio-Montiel
Publisher(s):
Elsevier BV
Tags:
Mathematics
article description
A graph is chordal if every induced cycle has three vertices. The Hadwiger number is the order of the largest complete minor of a graph. We characterize the chordal graphs in terms of the Hadwiger number and we also characterize the families of graphs such that for each induced subgraph H, (1) the Hadwiger number of H is equal to the maximum clique order of H, (2) the Hadwiger number of H is equal to the achromatic number of H, (3) the b -chromatic number is equal to the pseudoachromatic number, (4) the pseudo- b -chromatic number is equal to the pseudoachromatic number, (5) the Hadwiger number of H is equal to the Grundy number of H, and (6) the b -chromatic number is equal to the pseudo-Grundy number.

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