The adaptable choosability number grows with the choosability number

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Abstract

The adaptable choosability number of a multigraph G, denoted c ha(G), is the smallest integer k such that every edge labeling of G and assignment of lists of size k to the vertices of G permits a list coloring of G in which no edge e=uv has both u and v colored with the label of e. We show that c ha grows with ch, i.e. there is a function f tending to infinity such that c ha(G)<f(ch(G)). © 2011 Elsevier B.V. All rights reserved.

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Molloy, M., & Thron, G. (2011). The adaptable choosability number grows with the choosability number. Discrete Mathematics, 311(20), 2268–2271. https://doi.org/10.1016/j.disc.2011.06.016

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