On Balanced Coloring Games in Random Graphs

Consider the balanced Ramsey game, in which a player has r colors and where in each round r random edges of an initially empty graph on n vertices are presented. The player has to immediately assign a different color to each edge and her goal is to avoid creating a monochromatic copy of some fixed g...

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Bibliographic Details
Published inElectronic notes in discrete mathematics Vol. 38; pp. 425 - 430
Main Authors Gugelmann, Luca, Spöhel, Reto
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2011
Subjects
Coloring games
Ramsey theory
random graphs
Coloring games
Ramsey theory
random graphs
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Summary:Consider the balanced Ramsey game, in which a player has r colors and where in each round r random edges of an initially empty graph on n vertices are presented. The player has to immediately assign a different color to each edge and her goal is to avoid creating a monochromatic copy of some fixed graph F for as long as possible. The Achlioptas game is similar, but the player only loses when she creates a copy of F in one distinguished color. We show that there is an infinite family of nonforests F for which the balanced Ramsey game has a different threshold than the Achlioptas game, settling an open question by Krivelevich et al. We also consider the natural vertex analogues of both games and show that their thresholds coincide for all graphs F, in contrast to our results for the edge case.
ISSN:1571-0653
1571-0653
DOI:10.1016/j.endm.2011.09.069