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RSA
2011
14 years 4 months ago
2011
: The classical result in the theory of random graphs, proved by Erd˝os and Rényi in 1960, concerns the threshold for the appearance of the giant component in the random graph pr...
COMBINATORICS
2002
14 years 9 months ago
2002
A graph is f-choosable if for every collection of lists with list sizes specified by f there is a proper coloring using colors from the lists. The sum choice number is the minimum...
JGT
2010
14 years 8 months ago
2010
We show that every plane graph with maximum face size four whose all faces of size four are vertex-disjoint is cyclically 5-colorable. This answers a question of Albertson whether...
DM
2002
14 years 9 months ago
2002
We investigate the minimum and maximum number of colors in edge-colorings of Kn,n such that every copy of Kp,p receives at least q and at most q colors. Along the way we improve t...
JCT
2011
14 years 4 months ago
2011
This article is devoted to the study of continuous colorings of the n-element subsets of a Polish space. The homogeneity number hm(c) of an n-coloring c : [X]n → 2 is the least s...