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» On the Grundy Number of a Graph
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SIAMDM
2010
170views more  SIAMDM 2010»
13 years 2 months ago
Complete Minors and Independence Number
Let G be a graph with n vertices and independence number . Hadwiger's conjecture implies that G contains a clique minor of order at least n/. In 1982, Duchet and Meyniel prov...
Jacob Fox
GC
2007
Springer
13 years 7 months ago
On the Maximum Number of Cliques in a Graph
A clique is a set of pairwise adjacent vertices in a graph. We determine the maximum number of cliques in a graph for the following graph classes: (1) graphs with n vertices and m ...
David R. Wood
SPDP
1991
IEEE
13 years 11 months ago
Fault-tolerant meshes with minimal numbers of spares
This paper presents several techniques for adding fault-tolerance to distributed memory parallel computers. More formally, given a target graph with n nodes, we create a fault-tol...
Jehoshua Bruck, Robert Cypher, Ching-Tien Ho
COMPGEOM
2010
ACM
14 years 21 days ago
Adding one edge to planar graphs makes crossing number hard
A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show that it is NP-hard to compute the crossing number of near-planar graphs. The main idea ...
Sergio Cabello, Bojan Mohar
CORR
2006
Springer
128views Education» more  CORR 2006»
13 years 7 months ago
The Shannon capacity of a graph and the independence numbers of its powers
The independence numbers of powers of graphs have been long studied, under several definitions of graph products, and in particular, under the strong graph product. We show that t...
Noga Alon, Eyal Lubetzky