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Factorizations of regular graphs

✍ Scribed by Cun-Quan Zhang; Yong-Jin Zhu


Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
860 KB
Volume
56
Category
Article
ISSN
0095-8956

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It is shown that for each r G 3, a random r-regular graph on 2 n vertices is equivalent in a certain sense to a set of r randomly chosen disjoint perfect matchings of the 2 n vertices, as n Βͺ Ο±. This equivalence of two sequences of probabilistic spaces, called contiguity, occurs when all events almo

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A p-factor of a graph G is a regular spanning subgraph of degree p . For G regular of degree d ( G ) and order 2n, let ( p l , ..., p,) be a partition of d ( G ) , so that p i > 0 ( I S i S r ) and p , i i pr = d(G). If H I . ..., H, are edge-disjoint regular spanning subgraphs of G of degrees p I ,

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Given r 3 3 and 1 s A s r, we determine all values of k for which every r-regular graph with edge-connectivity A has a k-factor. Some of the earliest results in graph theory are due to Petersen [8] and concern factors in graphs. Among others, Petersen proved that a regular graph of even degree has a

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On the basis of the observation that a 3-regular graph has a perfect matching if and only if its line graph has a triangle-free 2 -factorisation, we show that a connected 4-regular graph has a triangle-free 2 -factorisation, provided it has no more than two cut-vertices belonging to a triangle. This