The interactive sum choice number of graphs

Bonamy, M. and Meeks, K. (2021) The interactive sum choice number of graphs. Discrete Applied Mathematics, 292, pp. 72-84. (doi: 10.1016/j.dam.2021.01.003)

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

Creator Roles

Meeks, K.: Data curation, Formal analysis, Investigation, Methodology, Writing – original draft, Writing – review and editing

• Authors: Bonamy, M., and Meeks, K.
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Discrete Applied Mathematics
• Publisher: Elsevier
• ISSN: 0166-218X
• ISSN (Online): 1872-6771
• Published Online: 16 January 2021
• Copyright Holders: Copyright © 2021 Elsevier B.V.
• First Published: First published in Discrete Applied Mathematics 292:72-84
• Publisher Policy: Reproduced in accordance with the publisher copyright policy