完全图分解为八边五边形连通单环图

Indonesian Journal of Combinatorics Pub Date : 2019-06-30 DOI:10.19184/IJC.2019.3.1.3

D. Froncek, O'Neill Kingston

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引用次数: 2

摘要

完全图Kn的G分解是Kn的一对边不相交子图族，它们都与G同构，使得Kn的每条边都属于G的一个副本。利用1967年由Rosa引入的基于ρ-标记的标准分解技术及其修正，我们证明了只要满足必要条件，10个有8条边包含五边形的非同构连通单环图中的每一个都分解了完全图Kn。

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Decomposition of complete graphs into connected unicyclic graphs with eight edges and pentagon

A G-decomposition of the complete graph K_n is a family of pairwise edge disjoint subgraphs of K_n, all isomorphic to G, such that every edge of K_n belongs to exactly one copy of G. Using standard decomposition techniques based on ρ-labelings, introduced by Rosa in 1967, and their modifications we show that each of the ten non-isomorphic connected unicyclic graphs with eight edges containing the pentagon decomposes the complete graph K_n whenever the necessary conditions are satisfied.

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Indonesian Journal of Combinatorics

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