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Almost resolvable Pk-decompositions of complete graphs

✍ Scribed by Min-Li Yu

Publisher: John Wiley and Sons
Year: 1991
Tongue: English
Weight: 925 KB
Volume: 15
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190150506

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✦ Synopsis

Abstract

An almost P~k~‐factor of G is a P~k~‐factor of G ‐ {v} for some vertex v. An almost resolvable P~k~‐decomposition of λ__K__~n~ is a partition of the edges of λ__K__~n~ into almost P~k~‐factors. We prove that necessary and sufficient conditions for the existence of an almost resolvable P~k~‐decomposition of λ__K__~n~ are n ≡ 1 (mod k) and λnk/2 ≡ 0 (mod k −1).

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