Two Hamiltonian cycles

TL;DR

This paper investigates the structure of graphs whose line graphs can be decomposed into exactly two Hamiltonian cycles, providing a characterization for such graphs.

Contribution

It offers a complete characterization of graphs whose line graphs decompose into two Hamiltonian cycles, addressing a specific case of a broader decomposition problem.

Findings

Characterization of graphs with line graphs decomposing into two Hamiltonian cycles

Conditions under which a graph's line graph can be split into two Hamiltonian cycles

Extension of known results on Hamiltonian decompositions

Abstract

If the line graph of a graph $G$ decomposes into Hamiltonian cycles, what is $G$? We answer this question for decomposition into two cycles.