3-consecutive Edge Coloring of a Graph

Three edges e1, e2 and e3 in a graph G are consecutive if they form a path (in this order) or a cycle of length 3. The 3 -consecutive edge coloring number ψ′ 3c(G) of G is the maximum number of colors permitted in a coloring of the edges of G such that if e1, e2 and e3 are consecutive edges in G, then e1 or e3 receives the color of e2. Here we initiate the study of ψ′ 3c(G). A close relation between 3 -consecutive edge colorings and a certain kind of vertex cuts is pointed out, and general bounds on ψ′ 3c are given in terms of other graph invariants. Algorithmically, the distinction between ψ′ 3c = 1 and ψ ′ 3c = 2 is proved to be intractable, while efficient algorithms are designed for some particular graph classes. AMS Subject Classification 05c15