List strong edge-coloring of graphs with maximum degree 4

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On strong edge-coloring of graphs with maximum degree 4

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a(G). It was conjectured by Alon, Sudakov and Zaks that for any simple and finite graph G, a(G) ≤ ∆+ 2, where ∆ = ∆(G) denotes the maximum degree of G. ...

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Strong edge-coloring of graphs with maximum degree 4 using 22 colors

In 1985, Erdős and Neśetril conjectured that the strong edge-coloring number of a graph is bounded above by 5 4 ∆ 2 when ∆ is even and 1 4 (5∆ 2 − 2∆ + 1) when ∆ is odd. They gave a simple construction which requires this many colors. The conjecture has been verified for ∆ ≤ 3. For ∆ = 4, the conjectured bound is 20. Previously, the best known upper bound was 23 due to Horak. In this paper we g...

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A Strong Edge-Coloring of Graphs with Maximum Degree 4 Using 22 Colors

In 1985, Erdős and Neśetril conjectured that the strong edge-coloring number of a graph is bounded above by 4 ∆ 2 when ∆ is even and 1 4 (5∆ 2 − 2∆ + 1) when ∆ is odd. They gave a simple construction which requires this many colors. The conjecture has been verified for ∆ ≤ 3. For ∆ = 4, the conjectured bound is 20. Previously, the best known upper bound was 23 due to Horak. In this paper we giv...

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Edge-face coloring of plane graphs with maximum degree nine

An edge-face colouring of a plane graph with edge set E and face set F is a colouring of the elements of E ∪ F so that adjacent or incident elements receive different colours. Borodin [Simultaneous coloring of edges and faces of plane graphs, Discrete Math., 128(1-3):21–33, 1994] proved that every plane graph of maximum degree ∆ > 10 can be edge-face coloured with ∆ + 1 colours. We extend Borod...

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List strong edge coloring of some classes of graphs

A strong edge coloring of a graph is a proper edge coloring in which every color class is an induced matching. The strong chromatic index of a graph is the minimum number of colors needed to obtain a strong edge coloring. In an analogous way, we can define the list version of strong edge coloring and list version of strong chromatic index. In this paper we prove that if G is a graph with maximu...

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ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 2020

ISSN: 0012-365X

DOI: 10.1016/j.disc.2020.111854