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.
- Balanced complete bipartite graph
- Complete graph
- Linear k-arboricity
- Linear k-forest