## Abstract An __n__βvertex graph is called pancyclic if it contains a cycle of length __t__ for all 3β€__t__β€__n__. In this article, we study pancyclicity of random graphs in the context of resilience, and prove that if __p__>__n__^β1/2^, then the random graph __G__(__n, p__) a.a.s. satisfies the f
Subgraphs of Random Match-Graphs
β Scribed by Jerzy Jaworski; Zbigniew Palka
- Publisher
- Springer Japan
- Year
- 2001
- Tongue
- English
- Weight
- 117 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0911-0119
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## Abstract We shall prove that if __L__ is a 3βchromatic (so called βforbiddenβ) graph, and β__R__^__n__^ is a random graph on __n__ vertices, whose edges are chosen independently, with probability __p__, and β__B__^__n__^ is a bipartite subgraph of __R__^__n__^ of maximum size, β__F__^__n__^ is a
The subject of this paper is the size of the largest component in random subgraphs of Cayley graphs, X n , taken over a class of p-groups, G n . G n consists of p-groups, G n , with the following properties: , where K is some positive constant. We consider Cayley graphs X n = (G n , S n ), where S