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Strong Edge-Coloring Of Planar Graphs
Discussiones Mathematicae Graph Theory, 2017 A strong edge-coloring of a graph is a proper edge-coloring where each color class induces a matching. We denote by 𝜒's(G) the strong chromatic index of G which is the smallest integer k such that G can be strongly edge-colored with k colors. It is known
Song Wen-Yao, Miao Lian-Ying
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From Edge-Coloring to Strong Edge-Coloring [PDF]
The Electronic Journal of Combinatorics, 2015 In this paper we study a generalization of both proper edge-coloring and strong edge-coloring: $k$-intersection edge-coloring, introduced by Muthu, Narayanan and Subramanian. In this coloring, the set $S(v)$ of colors used by edges incident to a vertex $v$ does not intersect $S(u)$ on more than $k$ colors when $u$ and $v$ are adjacent.
Borozan, Valentin +6 more
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On the Adjacent Strong Equitable Edge Coloring of Pn ∨ Pn, Pn ∨ Cn and Cn ∨ Cn
MATEC Web of Conferences, 2016 A proper edge coloring of graph G is called equitable adjacent strong edge coloring if colored sets from every two adjacent vertices incident edge are different,and the number of edges in any two color classes differ by at most one,which the required ...
Liu Jun +4 more
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Strong List Edge Coloring of Subcubic Graphs [PDF]
Mathematical Problems in Engineering, 2013 We study strong list edge coloring of subcubic graphs, and we prove that every subcubic graph with maximum average degree less than 15/7, 27/11, 13/5, and 36/13 can be strongly list edge colored with six, seven, eight, and nine colors, respectively.
Hongping Ma +4 more
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Strong edge colorings of graphs
Discrete Mathematics, 1996 The strong coloring number of a graph \(G\), \(\chi_s'(G)\), is the minimum number of colors for which there is a proper edge-coloring of \(G\) so that no two vertices are incident to edges having the same set of colors. (It is assumed that \(G\) has no isolated edges and at most one isolated vertex.) {Burris} and Schelp [J.
Odile Favaron +2 more
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Strong edge colorings of uniform graphs
Discrete Mathematics, 2004 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 \(\chi_S(G)\) of a graph \(G\) is the minimum number of colors in a strong edge coloring of \(G\). For a bipartite graph \(G=(U\cup V, E)\), and for two nonempty sets \(U'\subseteq U\) and \(V'\subseteq V\), let ...
Andrzej Czygrinow, Brendan Nagle
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Recent progress on strong edge-coloring of graphs
Discrete Mathematics, Algorithms and Applications, 2019 A strong edge-coloring of a graph [Formula: see text] is a partition of its edge set [Formula: see text] into induced matchings. In this paper, we gave a short survey on recent results about strong edge-coloring of a graph.
Kecai Deng, Gexin Yu, Xiangqian Zhou
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Between proper and strong edge‐colorings of subcubic graphs [PDF]
Journal of Graph Theory, 2020 AbstractIn a proper edge‐coloring the edges of every color form a matching. A matching is induced if the end‐vertices of its edges induce a matching. A strong edge‐coloring is an edge‐coloring in which the edges of every color form an induced matching.
Hervé Hocquard +2 more
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List Strong Edge-Colorings of Sparse Graphs
Bulletin of the Malaysian Mathematical Sciences Society, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Deng, Kecai +3 more
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Strong edge colorings of graphs and the covers of Kneser graphs [PDF]
Journal of Graph Theory, 2022 AbstractA proper edge coloring of a graph is strong if it creates no bichromatic path of length three. It is well known that for a strong edge coloring of a ‐regular graph at least colors are needed. We show that a ‐regular graph admits a strong edge coloring with colors if and only if it covers the Kneser graph .
Borut Luzar +3 more
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