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Decomposing edge-coloured graphs under colour degree constraints

Part of: Graph theory

Published online by Cambridge University Press:  01 March 2019

Shinya Fujita ,
Ruonan Li  and
Guanghui Wang
Shinya Fujita
Affiliation:
School of Date Science, Yokohama City University, 22-2, Seto, Kanazawa-ku, Yokohama, 236-0027Japan
Ruonan Li
Affiliation:
Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710072, PR China, Xi’an-Budapest Joint Research Center for Combinatorics, Northwestern Polytechnical University, Xi’an, 710129, PR China and Faculty of EEMCS, University of Twente, PO box 217, 7500 AE Enschede, The Netherlands
Guanghui Wang*
Affiliation:
School of Mathematics, Shandong University, Jinan, 250100, PR China
*
*Corresponding author. Email: [email protected]
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Abstract

For an edge-coloured graph G, the minimum colour degree of G means the minimum number of colours on edges which are incident to each vertex of G. We prove that if G is an edge-coloured graph with minimum colour degree at least 5, then V(G) can be partitioned into two parts such that each part induces a subgraph with minimum colour degree at least 2. We show this theorem by proving amuch stronger form. Moreover, we point out an important relationship between our theorem and Bermond and Thomassen’s conjecture in digraphs.

MSC classification

Primary: 05C15: Coloring of graphs and hypergraphs
Secondary: 05C20: Directed graphs (digraphs), tournaments
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 28 , Issue 5 , September 2019 , pp. 755 - 767
Copyright
© Cambridge University Press 2019 

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Footnotes

†

In this work, an extended abstract for the EUROCOMB 2017 (European Conference on Combinatorics, Graph Theory and Applications, 2017) conference proceedings has been published in [6].

‡

Supported by JSPS KAKENHI (no. 15K04979).

§

Supported by the Fundamental Research Funds for the Central Universities (no. 31020180QD124) and NSFC (no. 11671320, 11671429).

Supported by NSFC (no. 11871193, 11631014).

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