On the density of triangles and squares in regular finite and unimodular random graphs
β Scribed by Harangi, Viktor
- Book ID
- 121598901
- Publisher
- Springer-Verlag
- Year
- 2013
- Tongue
- English
- Weight
- 412 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0209-9683
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π SIMILAR VOLUMES
## Abstract Let __B(G)__ be the edge set of a bipartite subgraph of a graph __G__ with the maximum number of edges. Let __b~k~__ = inf{|__B(G)__|/|__E(G)__β__G__ is a cubic graph with girth at least __k__}. We will prove that lim~k β β~ __b~k~__ β₯ 6/7.
The asymptotic distribution of the number of cycles of length l in a random r-regular graph is determined. The length of the cycles is defined as a function of the Ε½ . Ε½ . number of vertices n, thus l s l n , and the length satisfies l n Βͺ Ο± as n Βͺ Ο±. The limiting Ε½ . Ε½ . distribution turns out to