Extension of Prescribed Linear Forests to Hamiltonian Decompositions

Determine whether every subgraph H of K_{2n+1} with n edges, whose edges are colored so that each color class induces a linear forest, admits an extension of that coloring to an n-coloring of K_{2n+1} in which every color class induces a Hamilton cycle.

Background

The paper recalls a conjecture of Javadi and Miralaei concerning the extension of a prescribed finite coloring of a subgraph of a complete graph. The required extension places each prescribed linear forest inside a distinct Hamilton cycle of a Hamiltonian decomposition. The paper proves an infinite analogue for K_ω using spanning double rays, but does not resolve the finite conjecture.