Distribution of certain sparse spanning subgraphs in random graphs

Details Distribution of certain sparse spanning subgraphs in random graphs Distribution of certain sparse spanning subgraphs in random graphs

2011-05-30

arxiv.org/abs/1105.5913v1

Mathematics

Combinatorics

22 pages, 3 figures

Scientific paper

We describe a general approach of determining the distribution of spanning subgraphs in the random graph $\G(n,p)$. In particular, we determine the distribution of spanning subgraphs of certain given degree sequences, which is a generalisation of the $d$-factors, of spanning triangle-free subgraphs, of (directed) Hamilton cycles and of spanning subgraphs that are isomorphic to a collection of vertex disjoint (directed) triangles.

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