# Circular chromatic index of graphs of maximum degree 3

@article{Afshani2005CircularCI,
title={Circular chromatic index of graphs of maximum degree 3},
author={Peyman Afshani and Mahsa Ghandehari and Mahya Ghandehari and Hamed Hatami and Ruzbeh Tusserkani and Xuding Zhu},
journal={Journal of Graph Theory},
year={2005},
volume={49}
}
• Published 1 August 2005
• Mathematics
• Journal of Graph Theory
This paper proves that if G is a graph (parallel edges allowed) of maximum degree 3, then χ′c(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 K  23 (the graph with three parallel edges between two vertices) and K4, respectively. As χ′c(H1) = χ′c(H2) = 4, our result implies that there is no graph G with 11/3 < χ′c(G) < 4. It also implies that if G is a 2‐edge connected cubic graph, then χ′c(G) ≤ 11/3. © 2005 Wiley…
21 Citations
• Mathematics
J. Graph Theory
• 2014
The circular chromatic index of a graph G, written χc′(G) , is the minimum r permitting a function c:E(G)→[0,r) such that 1≤c(e)−c(e′)≤r−1 whenever e and e′ are adjacent. It is known that for any
• Mathematics
• 2013
The circular chromatic index of a graph G is the infimum of all rational numbers p/q, such that there exists a circular p/q-edge-coloring of the graph G. A natural problem is to determine the set of
The circular chromatic number provides a more refined measure of colourability of graphs, than does the ordinary chromatic number. Thus circular colouring is of substantial importance wherever graph
• Mathematics
SIAM J. Discret. Math.
• 2010
The construction disproves a conjecture of Zhu that there is no bounded increasing infinite sequence in the set of circular chromatic indices of graphs and describes a sequence of graphs whose circular Chromatic indices converge to 3+1/3 from above.
One of the refinements of the chromatic index which has been recently investigated is the circular chromatic index. A circular edge-coloring of a graph G is a mapping c : E(G) → [0, r) satisfying 1 ≤
• Mathematics
• 2013
We introduce a new framework designed for constructing graphs with given circular chromatic index. This framework allows construction of graphs with arbitrary maximum degree and with additional
A circular $r$-edge-coloring of a graph $G$ is a mapping $c:E(G) o [0,r)$ such that for any two adjacent edges $e$ and $f$ of $G$ we have $1le |c(e)-c(f)|le r-1$. The circular chromatic index
The study of circular chromatic number Xc(G) of a graph G, which is a refinement of its chromaticNumber, has been very active in the past decade, and a glimpse of the recent progress is presented.

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It is shown that χ* < χ if and only if a particular digraph is acyclic and that the decisioin problem associated with this question is probably not in NP though it is both NP-hard and NP-easy.