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156
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JCT
2006
15 years 6 months ago
2006
One of Erdos' favourite conjectures was that any triangle-free graph G on n vertices should contain a set of n/2 vertices that spans at most n2/50 edges. We prove this when t...
188
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GC
2011
Springer
14 years 10 months ago
2011
Springer
The minimum clique partition (MCP) problem is that of partitioning the vertex set of a given graph into a minimum number of cliques. Given n points in the plane, the corresponding...
189
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COMBINATORICS
1998
15 years 6 months ago
1998
The aim of this paper is to give a coherent account of the problem of constructing cubic graphs with large girth. There is a well-defined integer µ0(g), the smallest number of v...
181
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STOC
2005
ACM
16 years 6 months ago
2005
ACM
We introduce a new graph parameter, called the Grothendieck constant of a graph G = (V, E), which is defined as the least constant K such that for every A : E R, sup f:V S|V |-1 ...
174
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SIAMDM
2008
15 years 6 months ago
2008
In this paper we consider the problem of testing whether a graph is triangle-free, and more generally, whether it is H-free, for a fixed subgraph H. The algorithm should accept gr...