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 \({h^2u(u-1)\equiv 0 \pmod {30}}\) , \({h(u-1)\equiv 0\pmod 3}\) , and u ≥ 3 with a definite exception (h, u) = (1, 10).
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Research supported by the National Natural Science Foundation of China under Grant No. 10971252, the Scientific-Technological Project of Nantong City under Grant No. K2009036, and the Program for the Innovation Talents of Nantong University.
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Wang, J., Ma, D. Petersen Graph Decompositions of Complete Multipartite Graphs. Graphs and Combinatorics 26, 737–744 (2010). https://doi.org/10.1007/s00373-010-0925-x
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DOI: https://doi.org/10.1007/s00373-010-0925-x