Approximate Hamilton Decompositions of Random Graphs

Details Approximate Hamilton Decompositions of Random Graphs Approximate Hamilton Decompositions of Random Graphs

2010-06-07

arxiv.org/abs/1006.1268v1

Mathematics

Combinatorics

15 pages

Scientific paper

We show that if pn >> log n, the binomial random graph G_{n,p} has an
approximate Hamilton decomposition. More precisely, we show that in this range
G_{n,p} contains a set of edge-disjoint Hamilton cycles covering almost all of
its edges. This is best possible in the sense that the condition that pn >> log
n is necessary.

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