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On the properties of weighted minimum colouring games

Hamers, Herbert, Horozoglu, Nayat ORCID: 0000-0002-4830-7015, Norde, Henk and Platz, Trine Tornøe (2022) On the properties of weighted minimum colouring games. Annals of Operations Research, 318 (2). 963 - 983. ISSN 0254-5330

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Identification Number: 10.1007/s10479-021-04374-9

Abstract

A weighted minimum colouring (WMC) game is induced by an undirected graph and a positive weight vector on its vertices. The value of a coalition in a WMC game is determined by the weighted chromatic number of its induced subgraph. A graph G is said to be globally (respectively, locally) WMC totally balanced, submodular, or PMAS-admissible, if for all positive integer weight vectors (respectively, for at least one positive integer weight vector), the corresponding WMC game is totally balanced, submodular or admits a population monotonic allocation scheme (PMAS). We show that a graph G is globally WMC totally balanced if and only if it is perfect, whereas any graph G is locally WMC totally balanced. Furthermore, G is globally (respectively, locally) WMC submodular if and only if it is complete multipartite (respectively, (2 K2, P4) -free). Finally, we show that G is globally PMAS-admissible if and only if it is (2 K2, P4) -free, and we provide a partial characterisation of locally PMAS-admissible graphs.

Item Type: Article
Official URL: https://www.springer.com/journal/10479
Additional Information: © 2022 The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Divisions: Management
Subjects: Q Science > QA Mathematics
H Social Sciences > HD Industries. Land use. Labor > HD28 Management. Industrial Management
Date Deposited: 18 Nov 2022 15:48
Last Modified: 18 Nov 2022 15:48
URI: http://eprints.lse.ac.uk/id/eprint/117367

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