Petersen Graph Decompositions of Complete Multipartite Graphs |
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Authors: | Jinhua Wang Dengju Ma |
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Institution: | (1) John’s University, Tamsui, Taipei Shien, Taiwan;(2) Department of Mathematics, Tamkang University, Tamsui, Taipei Shien, Taiwan; |
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Abstract: | Let P be the Petersen graph, and K
u(h) the complete multipartite graph with u parts of size h. A decomposition of K
u(h) into edge-disjoint copies of the Petersen graph P is called a P-decomposition of K
u(h) or a P-group divisible design of type h
u
. In this paper, we show that there exists a P-decomposition of K
u(h) if and only if h2u(u-1) o 0 mod 30{h^2u(u-1)\equiv 0 \pmod {30}} , h(u-1) o 0 mod 3{h(u-1)\equiv 0\pmod 3} , and u ≥ 3 with a definite exception (h, u) = (1, 10). |
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Keywords: | |
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