Suppose that two players take turns coloring the vertices of a given graph G with k colors. In each move the current player colors a vertex such that neighboring vertices get different colors. The first player wins this game if and only if at the end, all vertices are colored. The game chromatic number χg(G) is defined as the smallest k for which the first player has a winning strategy.Recently, Bohman, Frieze and Sudakov [Random Structures and Algorithms 2008] analysed the game chromatic number of random graphs and obtained lower and upper bounds of the same order of magnitude. In this paper we improve existing results and show that with high probability, the game chromatic number χg(Gn,p) of dense random graphs with p ≥ e-o(log n) is asymptotically twice as large as the ordinary chromatic number χ(Gn,p).
@article{10_37236_4391,
author = {Ralph Keusch and Angelika Steger},
title = {The game chromatic number of dense random graphs},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {4},
doi = {10.37236/4391},
zbl = {1305.05144},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4391/}
}
TY - JOUR
AU - Ralph Keusch
AU - Angelika Steger
TI - The game chromatic number of dense random graphs
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/4391/
DO - 10.37236/4391
ID - 10_37236_4391
ER -
%0 Journal Article
%A Ralph Keusch
%A Angelika Steger
%T The game chromatic number of dense random graphs
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/4391/
%R 10.37236/4391
%F 10_37236_4391
Ralph Keusch; Angelika Steger. The game chromatic number of dense random graphs. The electronic journal of combinatorics, Tome 21 (2014) no. 4. doi: 10.37236/4391
