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If H1,H2,…,Hk are edge-disjoint subgraphs of G such that E(G)=E(H1)∪E(H2)∪⋯∪E(Hk), then we say that H1,H2,…,Hk decompose G. If each Hi≅H, then we say that H decomposes G and we denote it by H|G. If each Hi is a closed trail, then the decomposition is called a closed trail decomposition of G. In this paper, we consider the decomposition of a complete equipartite graph with multiplicity λ, that is,...
In this paper, we consider resolvable k-cycle decompositions (for short, k-RCD) of Km×Kn, where × denotes the tensor product of graphs. It has been proved that the standard necessary conditions for the existence of a k-RCD of Km×Kn are sufficient when k is even.
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