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Packing tree factors in random and pseudo-random graphs | | Deepak Bal
; Alan Frieze
; Michael Krivelevich
; Po-Shen Loh
; | | Date: |
9 Apr 2013 | | 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 epsilon > 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 epsilon-fraction of its edges, as
long as epsilon^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. | | Source: | arXiv, 1304.2429 | | Services: | Forum | Review | PDF | Favorites | |
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