Waiter-Client Games on Randomly Perturbed Graphs

Publikationstyp
Journal Article
Date Issued
2021
Sprache
English
Author(s)
Clemens, Dennis  orcid-logo
Hamann, Fabian  orcid-logo
Mogge, Yannick  
Parczyk, Olaf  
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/10350
First published in
Trends in Mathematics  
Number in series
14
Start Page
397
End Page
403
Citation
Trends in Mathematics 14: 397-403 (2021)
Publisher DOI
10.1007/978-3-030-83823-2_62
Scopus ID
2-s2.0-85114087000
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.
Subjects
Connectivity
Hamilton cycles
Randomly perturbed graphs
Waiter-Client games