On k‐Edge‐Hamilton‐Connected Line Graphs

ABSTRACT We say that a graph is ‐edge‐Hamilton‐connected if has a Hamilton cycle containing all edges of for any with such that is a linear forest. In 2012, Kužel et al. conjectured that every 4‐connected line graph is 2‐edge‐Hamilton‐connected, and proved that it is equivalent to Thomassen's conjecture stating that every 4‐connected line graph is Hamiltonian. In this paper, we prove that for every ‐connected line graph is ‐edge‐Hamilton‐connected.