Linear k-Arboricity of Hypohamiltonian Graphs with Small Order

A linear k-forest is a forest which is composed by paths of length at most k. The linear k-arboricity of a graph G, denoted by la
_k
(G), is the least number of linear k-forests needed to decompose G. In this paper, we study the linear k-arboricity of Hypohamiltonian graphs with small order.