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Petersen Graph Decompositions of Complete Multipartite Graphs

✍ Scribed by Jinhua Wang; Dengju Ma


Publisher
Springer Japan
Year
2010
Tongue
English
Weight
163 KB
Volume
26
Category
Article
ISSN
0911-0119

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A fair hamilton decomposition of the complete multipartite graph G is a set of hamilton cycles in G whose edges partition the edges of G in such a way that, for each pair of parts and for each pair of hamilton cycles H 1 and H 2 , the difference in the number of edges in H 1 and H 2 joining vertices

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## Necessary conditions for IK(n, r), the complete multipartite graph with r parts of size n in which each edge has multiplicity 1, to have a P,-factorization are nr=O(mod k) and i(r-l)kn=O(mod2(k-1)). We show that when n=O(modk) or r=O(modk), these two conditions are also sufficient. (This impli