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On some factor theorems of graphs
β Scribed by Mao-cheng Cai
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 362 KB
- Volume
- 98
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
The aim of this note is to show that some recently published results on graph factors derive fairly easily from Lovrisz' (g,f)-factor theorems.
π SIMILAR VOLUMES
## Abstract A (__g__, __f__)βfactor of a graph is a subset __F__ of __E__ such that for all $v \in V$, $g(v)\le {\rm deg}\_{F}(v)\le f(v)$. Lovasz gave a necessary and sufficient condition for the existence of a (__g__, __f__)βfactor. We extend, to the case of edgeβweighted graphs, a result of Kano
On the basis of the observation that a 3-regular graph has a perfect matching if and only if its line graph has a triangle-free 2 -factorisation, we show that a connected 4-regular graph has a triangle-free 2 -factorisation, provided it has no more than two cut-vertices belonging to a triangle. This