List Total Colourings of Graphs

Authors:
M. Juvan;B. Mohar;R. Škrekovski
Affiliations:
Department of Mathematics, University of Ljubljana, Jadranska 19, 1111 Ljubljana, Slovenia (e-mail: martin.juvan@fmf.uni-lj.si, bojan.mohar@uni-lj.si, riste.skrekovski@fmf.uni-lj.si);Department of Mathematics, University of Ljubljana, Jadranska 19, 1111 Ljubljana, Slovenia (e-mail: martin.juvan@fmf.uni-lj.si, bojan.mohar@uni-lj.si, riste.skrekovski@fmf.uni-lj.si);Department of Mathematics, University of Ljubljana, Jadranska 19, 1111 Ljubljana, Slovenia (e-mail: martin.juvan@fmf.uni-lj.si, bojan.mohar@uni-lj.si, riste.skrekovski@fmf.uni-lj.si)
Venue:
Combinatorics, Probability and Computing
Year:
1998

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Abstract

We study the concept of list total colourings and prove that every multigraph of maximum degree 3 is 5-total-choosable. We also show that the total choice number of a graph of maximum degree 2 is equal to its total chromatic number.