On Hamilton cycle decompositions of the tensor product of complete graphs

C5-decompositions of the tensor product of complete graphs

Resolvable even cycle decompositions of the tensor product of complete graphs

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. © 2011 Elsevier B.V. All rights reserved.

A Note on Tensor Product of Graphs

Let $G$ and $H$ be graphs. The tensor product $Gotimes H$ of $G$ and $H$ has vertex set $V(Gotimes H)=V(G)times V(H)$ and edge set $E(Gotimes H)={(a,b)(c,d)| acin E(G):: and:: bdin E(H)}$. In this paper, some results on this product are obtained by which it is possible to compute the Wiener and Hyper Wiener indices of $K_n otimes G$.

Symmetric Hamilton cycle decompositions of complete multigraphs

Let n ≥ 3 and λ ≥ 1 be integers. Let λKn denote the complete multigraph with edge-multiplicity λ. In this paper, we show that there exists a symmetric Hamilton cycle decomposition of λK2m for all even λ ≥ 2 and m ≥ 2. Also we show that there exists a symmetric Hamilton cycle decomposition of λK2m − F for all odd λ ≥ 3 and m ≥ 2. In fact, our results together with the earlier results (by Walecki...

Fair Hamilton Decompositions of Complete Multipartite Graphs

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 H1 and H2, the difference in the number of edges in H1 and H2 joining vertices in these two parts is at most one. In this paper we completely settle the existence of such decomposi...