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Strong edge-coloring of $(3, Δ)$-bipartite graphs
Discret. Math., 2014 A strong edge-coloring of a graph $G$ is an assignment of colors to edges such that every color class induces a matching. We here focus on bipartite graphs whose one part is of maximum degree at most $3$ and the other part is of maximum degree $Δ$. For every such graph, we prove that a strong $4Δ$-edge-coloring can always be obtained.
Julien Bensmail +2 more
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Parity and strong parity edge-colorings of graphs
Journal of Combinatorial Optimization, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hsiang-Chun Hsu, Gerard J. Chang
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Distance-Local Rainbow Connection Number
Discussiones Mathematicae Graph Theory, 2022 Under an edge coloring (not necessarily proper), a rainbow path is a path whose edge colors are all distinct. The d-local rainbow connection number lrcd(G) (respectively, d-local strong rainbow connection number lsrcd(G)) is the smallest number of colors
Septyanto Fendy, Sugeng Kiki A.
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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.
Saeed Akbari, Hoda Bidkhori, N. Nosrati
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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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Characterizations of Graphs Having Large Proper Connection Numbers
Discussiones Mathematicae Graph Theory, 2016 Let G be an edge-colored connected graph. A path P is a proper path in G if no two adjacent edges of P are colored the same. If P is a proper u − v path of length d(u, v), then P is a proper u − v geodesic. An edge coloring c is a proper-path coloring of
Lumduanhom Chira +2 more
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On Proper (Strong) Rainbow Connection of Graphs
Discussiones Mathematicae Graph Theory, 2021 A path in an edge-colored graph G is called a rainbow path if no two edges on the path have the same color. The graph G is called rainbow connected if between every pair of distinct vertices of G, there is a rainbow path.
Jiang Hui +3 more
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Some Equal Degree Graph Edge Chromatic Number
MATEC Web of Conferences, 2016 Let G(V, E) be a simple graph and k is a positive integer, if it exists a mapping of f, and satisfied with f(e1)≠6 = f(e2) for two incident edges e1,e2∉E(G), f(e1)≠6=f(e2), then f is called the k-proper-edge coloring of G(k-PEC for short).
Liu Jun +4 more
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The strong chromatic index of 1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer ScienceThe chromatic index $\chi'(G)$ of a graph $G$ is the smallest $k$ for which $G$ admits an edge $k$-coloring such that any two adjacent edges have distinct colors.
Yiqiao Wang +3 more
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Strong Chromatic Index Of Planar Graphs With Large Girth
Discussiones Mathematicae Graph Theory, 2014 Let Δ ≥ 4 be an integer. In this note, we prove that every planar graph with maximum degree Δ and girth at least 1 Δ+46 is strong (2Δ−1)-edgecolorable, that is best possible (in terms of number of colors) as soon as G contains two adjacent vertices of ...
Jennhwa Chang Gerard +3 more
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