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» The Alcuin Number of a Graph
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IPPS
2007
IEEE
14 years 2 months ago
Minimum number of wavelengths equals load in a DAG without internal cycle
Let P be a family of dipaths. The load of an arc is the number of dipaths containing this arc. Let π(G, P) be the maximum of the load of all the arcs and let w(G, P) be the minim...
Jean-Claude Bermond, Michel Cosnard
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
JGT
2010
117views more  JGT 2010»
13 years 6 months ago
An approximate version of Hadwiger's conjecture for claw-free graphs
Hadwiger’s conjecture states that every graph with chromatic number χ has a clique minor of size χ. In this paper we prove a weakened version of this conjecture for the class ...
Maria Chudnovsky, Alexandra Ovetsky Fradkin
CORR
2006
Springer
128views Education» more  CORR 2006»
13 years 8 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
GC
2008
Springer
13 years 8 months ago
On the Acyclic Chromatic Number of Hamming Graphs
An acyclic coloring of a graph G is a proper coloring of the vertex set of G such that G contains no bichromatic cycles. The acyclic chromatic number of a graph G is the minimum nu...
Robert E. Jamison, Gretchen L. Matthews