k-regular factors and semi-k-regular factors in bipartite graphs
β Scribed by Keiko Kotani
- Publisher
- Springer
- Year
- 1998
- Tongue
- English
- Weight
- 418 KB
- Volume
- 2
- Category
- Article
- ISSN
- 0218-0006
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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
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## 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.
## 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