On compact k-edge-colorings: A polynomial time reduction from linear to cyclic

A k-edge-coloring of a graph G=(V,E) is a function c that assigns an integer c(e) (called color) in {0,1,...,k-1} to every edge e@?E so that adjacent edges get different colors. A k-edge-coloring is linear compact if the colors on the edges incident to every vertex are consecutive. The problem k-LCCP is to determine whether a given graph admits a linear compact k-edge coloring. A k-edge-coloring is cyclic compact if for every vertex v there are two positive integers a"v,b"v in {0,1,...,k-1} such that the colors on the edges incident to v are exactly {a"v,(a"v+1)mod k,...,b"v}. The problem k-CCCP is to determine whether a given graph admits a cyclic compact k-edge coloring. We show that the k-LCCP with possibly imposed or forbidden colors on some edges is polynomially reducible to the k-CCCP when k>=12, and to the 12-CCCP when k<12.