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arXiv · 1304.2429

Packing tree factors in random and pseudo-random graphs

Deepak Bal·Alan Frieze·Michael Krivelevich·Po-Shen Loh
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Abstract

For a fixed graph H with t vertices, an H-factor of a graph G with n vertices, where t divides n, is a collection of vertex disjoint (not necessarily induced) copies of H in G covering all vertices of G. We prove that for a fixed tree T on t vertices and ε> 0, the random graph G_{n,p}, with n a multiple of t, with high probability contains a family of edge-disjoint T-factors covering all but an ε-fraction of its edges, as long as ε^4 n p >> (log n)^2. Assuming stronger divisibility conditions, the edge probability can be taken down to p > (C log n)/n. A similar packing result is proved also for pseudo-random graphs, defined in terms of their degrees and co-degrees.

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Deepak Bal, Alan Frieze, Michael Krivelevich, Po-Shen Loh. 2014-04-01. Packing tree factors in random and pseudo-random graphs. https://arxiv.org/abs/1304.2429

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