## 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.
Regular factors and eigenvalues of regular graphs
β Scribed by Gu, Xiaofeng
- Book ID
- 124112852
- Publisher
- Elsevier Science
- Year
- 2014
- Tongue
- English
- Weight
- 386 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0195-6698
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π SIMILAR VOLUMES
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
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.
We present sufficient conditions for a regular multipartite graph to have a regular factor. These conditions are best possible