Circular chromatic index of graphs of maximum degree 3

Abstract

This paper proves that if G is a graph (parallel edges allowed) of maximum degree 3, then 0 c (G) 11=3 provided that G does not contain H 1 or H 2 as a subgraph, where H 1 and H 2 are obtained by subdividing one edge of K 3 2 (the graph with three parallel edges between two vertices) and K 4 , respectively. As

Circular chromatic index of type 1 Blanuša snarks

“…As indicated in Figure 2, using m copies of the block B, arranging them cyclically and joining them with an edge uv we obtain the graph B In this article we focus on the family B 1 . As a first step we examine why B 1 m is a snark.…”

Circular chromatic indices of even degree regular graphs

“…The circular chromatic index of snarks has been studied in [1,[4][5][6]14], and the circular chromatic index of Cartesian product graphs has been studied in [18]. Nevertheless, the question as which real numbers are the circular chromatic indices of graphs remains largely open.…”

“…Thus we have χ ′ (G) − 1 < χ ′ c (G) ≤ χ ′ (G), and χ ′ c is a refinement of χ ′ . The circular chromatic indices of graphs have been studied in many papers [1,[3][4][5][6][8][9][10][12][13][14]16,18]. It is known that for a subcubic multigraph G, either χ ′ c (G) = 4 or χ ′ c (G) ≤ 11/3 [1]; subcubic graphs G of girth at least six have χ ′ c (G) ≤ 7/2 [10]; graphs G of large girth have χ ′ c (G) close to ∆(G) [9]; for any integers k ≥ 4, 1 ≤ a ≤ k/2, p ≥ 2a 2…”

Circular chromatic index of Cartesian products of graphs

“…It was proved in [2] that all 2-edge-connected graphs with maximum degree at most 3 have circular chromatic index at most 11/3, except for two small graphs with circular chromatic index 4. In [5], it was proved that 2-edge-connected 3-regular graphs of large girth have circular chromatic index close to 3.…”