Regular factors in regular graphs
β Scribed by P. Katerinis
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 473 KB
- Volume
- 113
- Category
- Article
- ISSN
- 0012-365X
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β¦ Synopsis
Katerinis, P., Regular factors in regular graphs, Discrete Mathematics 113 (1993) 269-274.
Let G be a k-regular, (k -I)-edge-connected graph with an even number of vertices, and let m be an integer such that 1~ m s k -1. Then the graph obtained by removing any k -m edges of G, has an m-factor.
π SIMILAR VOLUMES
Let G be a 2r-regular, 2r-edge-connected graph of odd order and m be an integer such that 1 2rw(W)+2ec(S',S')-2 c d,-&)+2rlS'I. ES' (12) But CxsS' ## dc-o(x)=&sS dG-D(x)+dc-&)=CXEs dG,-D(x)+e&,S)+dG-&). Thus (12) implies, ## 2rIDI>2ro(W)+2eG(S',S')-2 c dc,-o(x)+e,(u,S)+d,-,(u) +WS'I. XC.7
In this paper the expectation and variance of the number of 2-factors in random r-regular graphs for any fixed r 2 3 is analyzed and the asymptotic distribution of this variable is determined.
## Abstract We show that every connected __K__~1,3~βfree graph with minimum degree at least __2k__ contains a __k__βfactor and construct connected __K__~1,3~βfree graphs with minimum degree __k__ + __0__(β__k__) that have no __k__βfactor.
We show that any k-regular bipartite graph with 2n vertices has at least \ (k&1) k&1 k k&2 + n perfect matchings (1-factors). Equivalently, this is a lower bound on the permanent of any nonnegative integer n\_n matrix with each row and column sum equal to k. For any k, the base (k&1) k&1 Γk k&2 is l
## Abstract A graph is said to be __K__~1,__n__~βfree, if it contains no __K__~1,__n__~ as an induced subgraph. We prove that for __n__ β©Ύ 3 and __r__ β©Ύ __n__ β1, if __G__ is a __K__~1,__n__~βfree graph with minimum degree at least (__n__^2^/4(__n__ β1))__r__ + (3__n__ β6)/2 + (__n__ β1)/4__r__, the