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» Critical Subgraphs of a Random Graph
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89
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COMBINATORICS
1999
102views more  COMBINATORICS 1999»
14 years 10 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
90
Voted
DAM
2008
134views more  DAM 2008»
14 years 10 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...
127
Voted
ENDM
2000
121views more  ENDM 2000»
14 years 10 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
79
Voted
WAW
2009
Springer
150views Algorithms» more  WAW 2009»
15 years 4 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