Edge-disjoint Hamilton cycles in graphs
نویسندگان
چکیده
منابع مشابه
Edge-disjoint Hamilton cycles in random graphs
We show that provided log n/n ≤ p ≤ 1 − n−1/4 log n we can with high probability find a collection of bδ(G)/2c edge-disjoint Hamilton cycles in G ∼ Gn,p, plus an additional edge-disjoint matching of size bn/2c if δ(G) is odd. This is clearly optimal and confirms, for the above range of p, a conjecture of Frieze and Krivelevich.
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In this paper we give an approximate answer to a question of Nash-Williams from 1970: we show that for every α > 0, every sufficiently large graph on n vertices with minimum degree at least (1/2 + α)n contains at least n/8 edge-disjoint Hamilton cycles. More generally, we give an asymptotically best possible answer for the number of edge-disjoint Hamilton cycles that a graph G with minimum degr...
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In the late 70s, it was shown by Komlós and Szemerédi ([7]) that for p = lnn+ln lnn+c n , the limit probability for G(n, p) to contain a Hamilton cycle equals the limit probability for G(n, p) to have minimum degree at least 2. A few years later, Ajtai, Komlós and Szemerédi ([1]) have shown a hitting time version of this in the G(n,m) model. Say a graph G has property H if it contains bδ(G)/2c ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2012
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2011.10.005