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On the facial Thue choice index of plane graphs
Authors:Jens Schreyer  Erika Škrabul’áková
Institution:1. Institute of Mathematics, Faculty of Mathematics and Natural Sciences, Ilmenau University of Technology, Ilmenau, Germany;2. Division of Applied Mathematics, BERG Faculty, Technical University of Ko?ice, Ko?ice, Slovakia
Abstract:Let G be a plane graph, and let φ be a colouring of its edges. The edge colouring φ of G is called facial non-repetitive if for no sequence r1,r2,,r2n, n1, of consecutive edge colours of any facial path we have ri=rn+i for all i=1,2,,n. Assume that each edge e of a plane graph G is endowed with a list L(e) of colours, one of which has to be chosen to colour e. The smallest integer k such that for every list assignment with minimum list length at least k there exists a facial non-repetitive edge colouring of G with colours from the associated lists is the facial Thue choice index of G, and it is denoted by πfl(G). In this article we show that πfl(G)291 for arbitrary plane graphs G. Moreover, we give some better bounds for special classes of plane graphs.
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