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Almost-regular factorization of graphs

✍ Scribed by Jin Akiyama; Mikio Kano

Publisher
John Wiley and Sons
Year
1985
Tongue
English
Weight
238 KB
Volume
9
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

For integers a and b, 0 s a s b, an [a,bl-graph G satisfies a s deg(x,G) s b for every vertex x of G, and an [a.bl-factor is a spanning subgraph

its edges can be decomposed into [a,bl-factors. When both k and tare positive integers and s is a nonnegative integer, w e prove that every [(12k + 2)t + 2ks, (12k + 4)t + 2ksl-graph is [2k,2k + 11-factorable. As its corollary, w e prove that every [r,r + 11-graph with r 3 12k2 + 2k is [2k,2k + 11factorable, which is a partial extension of the two results, one by Thomassen and the other by Era.

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