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COMBINATORICS
2004
108views more  COMBINATORICS 2004»
14 years 11 months ago
On the Chromatic Number of Intersection Graphs of Convex Sets in the Plane
Let G be the intersection graph of a finite family of convex sets obtained by translations of a fixed convex set in the plane. We show that every such graph with clique number k i...
Seog-Jin Kim, Alexandr V. Kostochka, Kittikorn Nak...
JGT
2007
87views more  JGT 2007»
14 years 11 months ago
A new upper bound on the cyclic chromatic number
A cyclic colouring of a plane graph is a vertex colouring such that vertices incident with the same face have distinct colours. The minimum number of colours in a cyclic colouring...
Oleg V. Borodin, Hajo Broersma, Alexei N. Glebov, ...
STOC
2006
ACM
116views Algorithms» more  STOC 2006»
16 years 1 days ago
Linear degree extractors and the inapproximability of max clique and chromatic number
: We derandomize results of H?astad (1999) and Feige and Kilian (1998) and show that for all > 0, approximating MAX CLIQUE and CHROMATIC NUMBER to within n1are NP-hard. We furt...
David Zuckerman
GC
2010
Springer
14 years 10 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
COMBINATORICA
2011
13 years 11 months ago
On the chromatic number of random geometric graphs
Given independent random points X1, . . . , Xn ∈ Rd with common probability distribution ν, and a positive distance r = r(n) > 0, we construct a random geometric graph Gn wi...
Colin McDiarmid, Tobias Müller