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.
Regular factors in regular multipartite graphs
β Scribed by Arne Hoffmann
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 226 KB
- Volume
- 5
- Category
- Article
- ISSN
- 1571-0653
No coin nor oath required. For personal study only.
β¦ Synopsis
We present sufficient conditions for a regular multipartite graph to have a regular factor. These conditions are best possible
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
## 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.
Let G be a 2r-regular, 2r-edge-connected graph of odd order and m be an integer such that 1 2rw(W)+2ec(S',S')-2 c d,-&)+2rlS'I. ES' (12) But CxsS' ## dc-o(x)=&sS dG-D(x)+dc-&)=CXEs dG,-D(x)+e&,S)+dG-&). Thus (12) implies, ## 2rIDI>2ro(W)+2eG(S',S')-2 c dc,-o(x)+e,(u,S)+d,-,(u) +WS'I. XC.7