Given r 3 3 and 1 s A s r, we determine all values of k for which every r-regular graph with edge-connectivity A has a k-factor. Some of the earliest results in graph theory are due to Petersen [8] and concern factors in graphs. Among others, Petersen proved that a regular graph of even degree has a
Regular factors of line graphs
β Scribed by Tsuyoshi Nishimura
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 244 KB
- Volume
- 85
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
We show that if m 3 2 is an even integer and G is a graph such that d,(v) L m + 1 for all vertices v in G, then the line graph L(G) of G has a 2m-factor;
and that if m is a nonnegative integer and G is a connected graph with jE(G)l even such that d,(v) 3 m + 2 for all vertices v in G, then the line graph L(G) has a (2m + 1)-factor.
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 In this article, we obtain a sufficient condition for the existence of regular factors in a regular graph in terms of its third largest eigenvalue. We also determine all values of __k__ such that every __r__βregular graph with the third largest eigenvalue at most has a __k__βfactor.
We present sufficient conditions for a regular multipartite graph to have a regular factor. These conditions are best possible