Circular chromatic index of graphs of maximum degree 3

الأصل · EN

This paper proves that if G is a graph (parallel edges allowed) of maximum degree 3, then χc'(G) ≤ 11/3 provided that G does not contain H₁ or H₂ as a subgraph, where H₁ and H₂ are obtained by subdividing one edge of K₂³ (the graph with three parallel edges between two vertices) and K₄, respectively. As χc'(H₁) = χc'(H₂) = 4, our result implies that there is no graph G with 11/3 < χc'(G) < 4. It also implies that if G is a 2-edge connected cubic graph, then χ'(G) ≤ 11/3.