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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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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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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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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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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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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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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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