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arXiv · 2004.01848

Bounds Related to The Edge-List Chromatic and Total Chromatic Numbers of a Simple Graph

M. Henderson·A. J. W. Hilton·R. Mary Jeya Jothi
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Abstract

We show that for a simple graph $G$, $c'(G)\leq\Delta(G)+2$ where $c'(G)$ is the choice index (or edge-list chromatic number) of $G$, and $\Delta(G)$ is the maximum degree of $G$. As a simple corollary of this result, we show that the total chromatic number $\chi_T(G)$ of a simple graph satisfies the inequality $\chi_T(G)\leq\ \Delta(G)+4$ and the total choice number $c_T(G)$ also satisfies this inequality. We also relate these bounds to the Hall index and the Hall condition index of a simple graph, and to the total Hall number and the total Hall condition number of a simple graph.

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M. Henderson, A. J. W. Hilton, R. Mary Jeya Jothi. 2020-04-04. Bounds Related to The Edge-List Chromatic and Total Chromatic Numbers of a Simple Graph. https://arxiv.org/abs/2004.01848

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