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Online Ramsey games for more than two colors
Author(s) -
Noever Andreas
Publication year - 2017
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20698
Subject(s) - monochromatic color , combinatorics , conjecture , graph , mathematics , enhanced data rates for gsm evolution , edge coloring , upper and lower bounds , discrete mathematics , computer science , line graph , artificial intelligence , graph power , mathematical analysis , botany , biology
Consider the following one‐player game played on an initially empty graph with n vertices. At each stage a randomly selected new edge is added and the player must immediately color the edge with one of r available colors. Her objective is to color as many edges as possible without creating a monochromatic copy of a fixed graph F . We use container and sparse regularity techniques to prove a tight upper bound on the typical duration of this game with an arbitrary, but fixed, number of colors for a family of 2‐balanced graphs. The bound confirms a conjecture of Marciniszyn, Spöhel and Steger and yields the first tight result for online graph avoidance games with more than two colors. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 464–492, 2017