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COMBINATORICS
1999
102views more  COMBINATORICS 1999»
13 years 4 months ago
Critical Subgraphs of a Random Graph
We prove that the threshold for a random graph to have a k-core is equal to the threshold for having a subgraph which meets a necessary condition of Gallai for being k-critical. 1...
Michael Molloy, Bruce A. Reed
DAM
2008
134views more  DAM 2008»
13 years 4 months ago
Efficient algorithms for finding critical subgraphs
This paper presents algorithms to find vertex-critical and edgecritical subgraphs in a given graph G, and demonstrates how these critical subgraphs can be used to determine the ch...
Christian Desrosiers, Philippe Galinier, Alain Her...
ENDM
2000
121views more  ENDM 2000»
13 years 4 months ago
Finding the chromatic number by means of critical graphs
We propose a new exact algorithm for finding the chromatic number of a graph G. The algorithm attempts to determine the smallest possible induced subgraph G' of G which has t...
Francine Herrmann, Alain Hertz
WAW
2009
Springer
150views Algorithms» more  WAW 2009»
13 years 11 months ago
The Giant Component in a Random Subgraph of a Given Graph
We consider a random subgraph Gp of a host graph G formed by retaining each edge of G with probability p. We address the question of determining the critical value p (as a function...
Fan Chung Graham, Paul Horn, Linyuan Lu