Pseudo-one-factorizations of regular graphs of odd order — II. products of graphs
✍ Scribed by Guo-Hui Zhang
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 693 KB
- Volume
- 128
- Category
- Article
- ISSN
- 0012-365X
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📜 SIMILAR VOLUMES
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 ª ϱ. This equivalence of two sequences of probabilistic spaces, called contiguity, occurs when all events almo
## Abstract Kotzig asked in 1979 what are necessary and sufficient conditions for a __d__‐regular simple graph to admit a decomposition into paths of length __d__ for odd __d__>3. For cubic graphs, the existence of a 1‐factor is both necessary and sufficient. Even more, each 1‐factor is extendable
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 ,
## Abstract We consider one‐factorizations of __K__~2__n__~ possessing an automorphism group acting regularly (sharply transitively) on vertices. We present some upper bounds on the number of one‐factors which are fixed by the group; further information is obtained when equality holds in these boun
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