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» On the Chromatic Number of Random Graphs
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DM
2006
79views more  DM 2006»
15 years 3 months ago
Conditional colorings of graphs
For an integer r > 0, a conditional (k, r)-coloring of a graph G is a proper k-coloring of the vertices of G such that every vertex of degree at least r in G will be adjacent t...
Hong-Jian Lai, Jianliang Lin, Bruce Montgomery, Ta...
COMBINATORICA
2008
130views more  COMBINATORICA 2008»
15 years 3 months ago
Two-point concentration in random geometric graphs
A random geometric graph Gn is constructed by taking vertices X1, . . . , Xn Rd at random (i.i.d. according to some probability distribution with a bounded density function) and...
Tobias Müller
142
Voted
COMBINATORICS
2006
123views more  COMBINATORICS 2006»
15 years 3 months ago
The Non-Crossing Graph
Two sets are non-crossing if they are disjoint or one contains the other. The noncrossing graph NCn is the graph whose vertex set is the set of nonempty subsets of [n] = {1, . . ....
Nathan Linial, Michael E. Saks, David Statter
GC
2010
Springer
15 years 2 months ago
The b-Chromatic Number of Cubic Graphs
The b-chromatic number of a graph G is the largest integer k such that G admits a proper k-coloring in which every color class contains at least one vertex adjacent to some vertex...
Marko Jakovac, Sandi Klavzar
109
Voted
JGT
2011
90views more  JGT 2011»
14 years 10 months ago
On directed local chromatic number, shift graphs, and Borsuk-like graphs
Gábor Simonyi, Gábor Tardos