Acyclic edge colourings of graphs with large girth

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Generalised acyclic edge colourings of graphs with large girth

An edge colouring of a graph G is called acyclic if it is proper and every cycle contains at least three colours. We show that for every ε > 0, there exists a g = g(ε) such that if G has girth at least g then G admits an acyclic edge colouring with at most (1 + ε)∆ colours.

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Acyclic Colourings of Planar Graphs with Large Girth

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About acyclic edge colourings of planar graphs

Let G = (V,E) be any finite simple graph. A mapping C : E → [k] is called an acyclic edge k-colouring of G, if any two adjacent edges have different colours and there are no bichromatic cycles in G. In other words, for every pair of distinct colours i and j, the subgraph induced by all the edges which have either colour i or j is acyclic. The smallest number k of colours, such that G has an acy...

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Total Colourings of Planar Graphs with Large Girth

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ژورنال

عنوان ژورنال: Random Structures & Algorithms

سال: 2016

ISSN: 1042-9832

DOI: 10.1002/rsa.20695