Circular chromatic index of type 1 Blanuša snarks
✍ Scribed by Ján Mazák
- Publisher
- John Wiley and Sons
- Year
- 2008
- Tongue
- English
- Weight
- 111 KB
- Volume
- 59
- Category
- Article
- ISSN
- 0364-9024
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✦ Synopsis
Abstract
We determine the exact value of the circular chromatic index of generalized Blanuša snarks of type 1 introduced by Watkins more than two decades ago. In this case, the index takes infinitely many values and can get arbitrarily close to 3. Generalized Blanuša snarks are the first explicit class with this property; until now only finitely many values of the circular chromatic index of snarks have been known. © 2008 Wiley Periodicals, Inc. J Graph Theory 59: 89–96, 2008
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## Abstract The __circular chromatic index__ of a graph __G__, written $\chi\_{c}'(G)$, is the minimum __r__ permitting a function $f : E(G)\rightarrow [0,r)$ such that $1 \le | f(e)-f(e')|\le r - 1$ whenever __e__ and $e'$ are incident. Let $G = H$ □ $C\_{2m +1}$, where □ denotes Cartesian product
## Abstract 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 __H__~1~ or __H__~2~ as a subgraph, where __H__~1~ and __H__~2~ are obtained by subdividing one edge of __K__ (the graph with three