New Bounds on the List-Chromatic Index of the Complete Graph and Other Simple Graphs

Authors:
Roland Häggkvist;Jeannette Janssen
Affiliations:
Department of Mathematics, University of Umeå, S-901 87 Umeå, Sweden (e-mail: haggkvist@mathdept.umu.se);Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, UK (e-mail: janssen@cdam.lse.ac.uk)
Venue:
Combinatorics, Probability and Computing
Year:
1997

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Abstract

In this paper we show that the list chromatic index of the complete graph Kn is at most n. This proves the list-chromatic conjecture for complete graphs of odd order. We also prove the asymptotic result that for a simple graph with maximum degree d the list chromatic index exceeds d by at most 𝒪(d2/3√log d).