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Waiter-Client games on randomly perturbed graphs

Clemens, Dennis, Hamann, Fabian, Mogge, Yannick and Parczyk, Olaf (2021) Waiter-Client games on randomly perturbed graphs. In: Nešetřil, Jaroslav, Perarnau, Guillem, Rué, Juanjo and Serra, Oriol, (eds.) Extended Abstracts EuroComb 2021: European Conference on Combinatorics, Graph Theory and Applications. Trends in Mathematics. Springer Science and Business Media Deutschland GmbH, Cham, CH, 397 - 403. ISBN 9783030838225

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Identification Number: 10.1007/978-3-030-83823-2_62

Abstract

Waiter-Client games are played on a hypergraph (X, F), where F⊆ 2X denotes the family of winning sets. During each round, Waiter offers a predefined amount (called bias) of elements from the board X, from which Client takes one for himself while the rest go to Waiter. Waiter wins the game if she can force Client to occupy any winning set F∈ F. In this paper we consider Waiter-Client games played on randomly perturbed graphs. These graphs consist of the union of a deterministic graph Gα on n vertices with minimum degree at least αn and the binomial random graph Gn , p. Depending on the bias we determine the order of the threshold probability for winning the Hamiltonicity game and the k-connectivity game on Gα∪ Gn , p.

Item Type: Book Section
Official URL: https://link.springer.com/book/10.1007/978-3-030-8...
Additional Information: © 2021 The Authors, under exclusive license to Springer Nature Switzerland AG.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 24 Mar 2022 12:36
Last Modified: 04 Apr 2022 13:09
URI: http://eprints.lse.ac.uk/id/eprint/114456

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