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Regular factors in regular multipartite graphs

✍ Scribed by Arne Hoffmann


Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
226 KB
Volume
5
Category
Article
ISSN
1571-0653

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✦ Synopsis


We present sufficient conditions for a regular multipartite graph to have a regular factor. These conditions are best possible


πŸ“œ SIMILAR VOLUMES


Regular factors in regular graphs
✍ P. Katerinis πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 473 KB

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.

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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

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Factors of regular graphs
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✍ P. Katerinis πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 258 KB

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