The linear k-arboricity of the Mycielski graph M(Kn)
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چکیده
A linear k-forest of an undirected graph G is a subgraph of G whose components are paths with lengths at most k. The linear k-arboricity Of G, denoted by lak(G), is the minimum number of linear k-forests needed to partition the edge set E(G) of G. In case that the lengths of paths are not restricted, we then have the linear arboricity ofG, denoted by la(G). In this paper, the exact values of the linear 3-arboricity and the linear arboricity of the Mycielski graph M(Kn), and the linear k-arboricity of the Mycielski graph M(Kn) when n is even and k ≥ 5, are obtained. Key–Words: Linear k-forest; linear k-arboricity; Mycielski graph; bipartite difference
منابع مشابه
The linear 3-arboricity of Kn, n and Kn
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. In this paper, we completely determine lak(G) when G is a balanced complete bipartite graph Kn,n or a complete graph Kn, and k = 3. © 2007 Elsevier B.V. All rights reserved.
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