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» Injective colorings of sparse graphs
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STOC
2002
ACM
121views Algorithms» more  STOC 2002»
15 years 12 months ago
Almost all graphs with average degree 4 are 3-colorable
We analyze a randomized version of the Brelaz heuristic on sparse random graphs. We prove that almost all graphs with average degree dp4:03; i.e., G?n; p ? d=n?; are 3-colorable a...
Dimitris Achlioptas, Cristopher Moore
MST
2010
98views more  MST 2010»
14 years 10 months ago
Why Almost All k-Colorable Graphs Are Easy to Color
Coloring a k-colorable graph using k colors (k ≥ 3) is a notoriously hard problem. Considering average case analysis allows for better results. In this work we consider the unif...
Amin Coja-Oghlan, Michael Krivelevich, Dan Vilench...
DM
2010
65views more  DM 2010»
14 years 11 months ago
Decomposition of sparse graphs, with application to game coloring number
Mickaël Montassier, Arnaud Pêcher, Andr...
SIAMDM
2010
99views more  SIAMDM 2010»
14 years 10 months ago
Edge-Injective and Edge-Surjective Vertex Labellings
For a graph G = (V, E) we consider vertex-k-labellings f : V → {1, 2, . . . , k} for which the induced edge weighting w : E → {2, 3, . . . , 2k} with w(uv) = f(u) + f(v) is inj...
Stephan Brandt, Jozef Miskuf, Dieter Rautenbach, F...