On the properties of weighted minimum colouring games
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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.
Original language | English |
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Journal | Annals of Operations Research |
Volume | 318 |
Pages (from-to) | 963–983 |
Number of pages | 21 |
ISSN | 0254-5330 |
DOIs | |
Publication status | Published - 2022 |
Bibliographical note
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
- (2 K, Complete multipartite graph, P) -free graph, Population monotonic allocation schemes, Submodularity, Totally balancedness, Weighted minimum colouring game
Research areas
ID: 300444574