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• W1762040488 abstract "We introduce a search game for two players played on a scenario consisting of a ground set together with a collection of feasible partitions. This general setting allows us to obtain new characterisations of many width parameters such as rank-width and carving-width of graphs, matroid tree-width and GF(4)-rank-width. We show that the game variant corresponds to a tree decomposition of the ground set along feasible partitions. Our framework also captures many other decompositions into simple subsets of the ground set, such as decompositions into planar subgraphs. Within our general framework, we take a step towards characterising search games. We exhibit a large class of monotone scenarios, i.e. of scenarios where the game and its variant coincide. As a consequence, determining the winner is in NP for these games. This result implies monotonicity for all our search games, that are equivalent to branch-width of a submodular function. Finally, we include a proof showing that the matroid tree-width of a graphic matroid is not larger than the tree-width of the corresponding graph. This proof is considerably shorter than the original proof and it is purely graph theoretic." @default.
• W1762040488 created "2016-06-24" @default.
• W1762040488 creator A5033412587 @default.
• W1762040488 date "2009-06-21" @default.
• W1762040488 modified "2023-09-27" @default.
• W1762040488 title "Games for width parameters and monotonicity" @default.
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• W1762040488 hasPublicationYear "2009" @default.
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