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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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Strong Edge-Coloring of Hamming Graphs
Proceedings of Computer Science and Information Technologies 2023 Conference, 2023 An edge coloring of a graph G is a mapping Á : EG ! N. The edge coloring Á is called strong if Áe 6= Áe0 for any two edges e and e0 that are distance at most one apart. The minimum number of colors needed for a strong edge coloring of a graph G is called strong chromatic index of G and denoted by Â0 sG.
Drambyan, A., Petrosyan, P.
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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.
Julien Bensmail +2 more
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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.
Herve Hocquard +2 more
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Rainbow connection number of Cm o Pn and Cm o Cn
Indonesian Journal of Combinatorics, 2020 Let G = (V(G),E(G)) be a nontrivial connected graph. A rainbow path is a path which is each edge colored with different color. A rainbow coloring is a coloring which any two vertices should be joined by at least one rainbow path.
Alfi Maulani +3 more
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The Strong 3-Rainbow Index of Graphs Containing Three Cycles
InPrime, 2023 The concept of a strong k-rainbow index is a generalization of a strong rainbow connection number, which has an interesting application in security systems in a communication network.
Zata Yumni Awanis
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r-Strong edge colorings of graphs
Discrete Mathematics, 2006 If \(G\) is a graph and \(n\) a natural number, \(\chi(G,n)\) denotes the minimum number of colours required for a proper edge colouring of \(G\) in which no two vertices with distance at most \(n\) are incident to edges coloured with the same set of colours.
Akbari, S., Bidkhori, H., Nosrati, N.
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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 ...
Hudák, Dávid +3 more
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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, Rachel Yu
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