The interactive sum choice number of graphs

Bonamy, M. and Meeks, K. (2017) The interactive sum choice number of graphs. Electronic Notes in Discrete Mathematics, 61, pp. 139-145. (doi:10.1016/j.endm.2017.06.031)

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Abstract

We introduce a variant of the well-studied sum choice number of graphs, which we call the interactive sum choice number. In this variant, we request colours to be added to the vertices' colour-lists one at a time, and so we are able to make use of information about the colours assigned so far to determine our future choices. The interactive sum choice number cannot exceed the sum choice number and we conjecture that, except in the case of complete graphs, the interactive sum choice number is always strictly smaller than the sum choice number. In this paper we provide evidence in support of this conjecture, demonstrating that it holds for a number of graph classes, and indeed that in many cases the difference between the two quantities grows as a linear function of the number of vertices.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Meeks, Dr Kitty
Authors: Bonamy, M., and Meeks, K.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Electronic Notes in Discrete Mathematics
Publisher:Elsevier
ISSN:1571-0653
ISSN (Online):1571-0653
Published Online:03 August 2017
Copyright Holders:Copyright © 2017 Elsevier B.V.
First Published:First published in Electronic Notes in Discrete Mathematics 61:139-145
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher
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