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A short proof of Catlin's extension of Brooks' theorem

✍ Scribed by John Mitchem

Publisher: Elsevier Science
Year: 1978
Tongue: English
Weight: 262 KB
Volume: 21
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(78)90092-4

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✦ Synopsis

Recently, in [3], Catlin proved the following extension of Brooks' Theorem [2]. T&eortln 1. Let G be u connected graph with muximcrm degree A(G) = h. If G is neither complete nor an odd cycle, then there exists an h-coloring of G with a monmhromatic maximum independent set. In addition to being of some interest for itself, Theorem 1, as Catlin pointed out, provides a proof of the following conjecture of Albertson, Bollob& and Tucker [ 11. Conjecture 2. If a graph H with A(H) = h does not contain Kh and H is neither of two specified graphs HI and Hz, then there is an h-colorzng of 14 such that me

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