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GC
2011
Springer
13 years 3 months ago
Properly Edge-Coloured Subgraphs in Colourings of Bounded Degree
The smallest n such that every colouring of the edges of Kn must contain a monochromatic star K1,s+1 or a properly edge-coloured Kt is denoted by f(s, t). Its existence is guarant...
Klas Markström, Andrew Thomason, Peter Wagner...
ALGORITHMICA
2004
150views more  ALGORITHMICA 2004»
13 years 8 months ago
Sum Coloring of Bipartite Graphs with Bounded Degree
We consider the Chromatic Sum Problem on bipartite graphs which appears to be much harder than the classical Chromatic Number Problem. We prove that the Chromatic Sum Problem is NP...
Michal Malafiejski, Krzysztof Giaro, Robert Jancze...
COMBINATORICA
2007
117views more  COMBINATORICA 2007»
13 years 8 months ago
Embedding nearly-spanning bounded degree trees
We derive a sufficient condition for a sparse graph G on n vertices to contain a copy of a tree T of maximum degree at most d on (1 − )n vertices, in terms of the expansion prop...
Noga Alon, Michael Krivelevich, Benny Sudakov
MFCS
2007
Springer
14 years 2 months ago
Uncover Low Degree Vertices and Minimise the Mess: Independent Sets in Random Regular Graphs
Abstract. We present algorithmic lower bounds on the size of the largest independent sets of vertices in a random d-regular graph. Our bounds hold with probability approaching one ...
William Duckworth, Michele Zito
MFCS
1995
Springer
14 years 9 days ago
Graph Inference from a Walk for TRees of Bounded Degree 3 is NP-Complete
The graph inference from a walk for a class C of undirected edge-colored graphs is, given a string x of colors, nding the smallest graph G in C that allows a traverse of all edge...
Osamu Maruyama, Satoru Miyano