Line k-Arboricity in Product Networks

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摘要：

A linear k-forest is a forest whose components are paths of length at most k. The linear k-arboricity of a graph G, denoted by lak(G), is the least number of linear k-forests needed to decompose G. Recently, Zuo, He, and Xue studied the exact values of the linear (nu22121)-arboricity of Cartesian products of various combinations of complete graphs, cycles, complete multipartite graphs. In this paper, for general k we show that max{lak(G),lal(H)}u2264lamax{k,l}(Gu25a1H)u2264lak(G)+lal(H) for any two graphs G and H. Denote by Gu2218H,u2009Gu00d7H and Gu22a0H the lexicographic product, direct product and strong product of two graphs G and H, respectively. For any two graphs G and H, we also derive upper and lower bounds of lak(Gu2218H),lak(Gu00d7H) and lak(Gu22a0H) in this paper. The linear k-arboricity of a 2-dimensional grid graph, a r-dimensional mesh, a r-dimensional torus, a r-dimensional generalized hypercube and a hyper Petersen network are also studied.

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关键词：

Linear k-forest linear k-arboricity Cartesian product lexicographic product strong product direct product

DOI：

10.1142/S0219265916500080

年份：

2016