k-factors in regular graphs
β Scribed by Wai Chee Shiu; Gui Zhen Liu
- Publisher
- Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2008
- Tongue
- English
- Weight
- 171 KB
- Volume
- 24
- Category
- Article
- ISSN
- 1439-7617
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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.
## 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
We present sufficient conditions for a regular multipartite graph to have a regular factor. These conditions are best possible