The Linear 2- and 4-Arboricity of Complete Bipartite Graph Km,n

الملخص EN

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 decompose G.

In case the lengths of paths are not restricted, we then have the linear arboricity of G, denoted by la(G).

In this paper, the exact value of the linear 2- and 4-arboricity of complete bipartite graph Km,n for some m and n is obtained.