Embedding k-Regular Graphs in k + 1-Regular Graphs
β Scribed by Gardiner, A.
- Book ID
- 120095342
- Publisher
- Oxford University Press
- Year
- 1983
- Tongue
- English
- Weight
- 171 KB
- Volume
- s2-28
- Category
- Article
- ISSN
- 0024-6107
No coin nor oath required. For personal study only.
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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