On the facial Thue choice index of plane graphs |
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Authors: | Jens Schreyer Erika Škrabul’áková |
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Affiliation: | 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 |
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Abstract: | Let be a plane graph, and let be a colouring of its edges. The edge colouring of is called facial non-repetitive if for no sequence , , of consecutive edge colours of any facial path we have for all . Assume that each edge of a plane graph is endowed with a list of colours, one of which has to be chosen to colour . The smallest integer such that for every list assignment with minimum list length at least there exists a facial non-repetitive edge colouring of with colours from the associated lists is the facial Thue choice index of , and it is denoted by . In this article we show that for arbitrary plane graphs . Moreover, we give some better bounds for special classes of plane graphs. |
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