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Color Code Techniques In Rainbow Connection [PDF]
Electronic Journal of Graph Theory and Applications, 2018 Let G be a graph with an edge k-coloring γ : E(G) → {1, …, k} (not necessarily proper). A path is called a rainbow path if all of its edges have different colors.
Septyanto, F. (Fendy) +1 more
core +3 more sources
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
doaj +3 more sources
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
exaly +2 more sources
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 ...
David Hudak +2 more
exaly +4 more sources
Strong Edge Coloring of Generalized Petersen Graphs
Mathematics, 2020 A strong edge coloring of a graph G is a proper edge coloring such that every color class is an induced matching. In 2018, Yang and Wu proposed a conjecture that every generalized Petersen graph P(n,k) with k≥4 and n>2k can be strong edge colored with ...
Lianying Miao
exaly +3 more sources
Adjacent strong edge coloring of graphs
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 ...
Zhongfu Zhang, Linzhong Liu
exaly +3 more sources
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
exaly +3 more sources
Strong edge-coloring for jellyfish graphs
Discrete Mathematics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gérard J Chang, Chi-Yün Hsu
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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.
Hong Zhu, Zhengke Miao
exaly +3 more sources
Strong edge-coloring of cubic bipartite graphs: A counterexample
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 W Cranston
exaly +4 more sources