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Strong edge coloring sparse graphs [PDF]
Electronic Notes in Discrete Mathematics, 2015 A strong edge coloring of a graph is a proper edge coloring such that no edge has two incident edges of the same color. Erdős and Nesetřil conjectured in 1989 that $5 /4∆2$ colors are always enough for a strong edge coloring, where $∆$ is the maximum degree of the graph.
Marthe Bonamy, Hervé Hocquard
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The strong edge-coloring for graphs with small edge weight
Discrete Mathematics, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gexin Yu, Xiangqian Zhou, Lily Chen
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Adjacent strong edge coloring of graphs [PDF]
Applied Mathematics Letters, 2002 A proper edge coloring of a graph is an adjacent strong edge coloring if, for every adjacent vertices \(u\) and \(v\), the set of colors of all edges at \(u\) is different from the set of all colors of edges at \(v\). The authors determine the minimum number \(k\) such that a tree (a cycle, a complete graph) has an adjacent strong edge coloring with ...
Linzhong Liu, Zhongfu Zhang
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Strong edge-coloring of 2-degenerate graphs
Discrete Applied Mathematics, 2023 A strong edge-coloring of a graph $G$ is an edge-coloring in which every color class is an induced matching, and the strong chromatic index $χ_s'(G)$ is the minimum number of colors needed in strong edge-colorings of $G$. A graph is $2$-degenerate if every subgraph has minimum degree at most $2$. Choi, Kim, Kostochka, and Raspaud (2016) showed $χ_s'(G)
Gexin Yu
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Strong edge-coloring of cubic bipartite graphs: A counterexample [PDF]
Discrete Applied Mathematics, 2022 A strong edge-coloring $φ$ of a graph $G$ assigns colors to edges of $G$ such that $φ(e_1)\ne φ(e_2)$ whenever $e_1$ and $e_2$ are at distance no more than 1. It is equivalent to a proper vertex coloring of the square of the line graph of $G$. In 1990 Faudree, Schelp, Gyárfás, and Tuza conjectured that if $G$ is a bipartite graph with maximum degree 3 ...
Daniel Cranston
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Strong edge-coloring of planar graphs
Discrete Mathematics, 2014 A strong edge coloring of a graph is a proper edge coloring where the edges at distance at most two receive distinct colors. It is known that every planar graph with maximum degree D has a strong edge coloring with at most 4D + 4 colors. We show that 3D + 6 colors suffice if the graph has girth 6, and 3D colors suffice if the girth is at least 7 ...
Riste Škrekovski +2 more
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On strong list edge coloring of subcubic graphs
Discrete Mathematics, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhengke Miao
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Strong edge-coloring of graphs with maximum degree 4 using 22 colors
Discrete Mathematics, 2006Daniel Cranston
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List strong edge-coloring of graphs with maximum degree 4
Discrete Mathematics, 2020Donglei Yang, Meijie Ma
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