Results 21 to 30 of about 4,925 (221)
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 Edge Coloring of Cayley Graphs and Some Product Graphs [PDF]
Graphs and Combinatorics, 2022 AbstractA strong edge coloring of a graph G is a proper edge coloring of G such that every color class is an induced matching. The minimum number of colors required is termed the strong chromatic index. In this paper we determine the exact value of the strong chromatic index of all unitary Cayley graphs.
Suresh Dara +3 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.
Favaron, Odile, Li, Hao, Schelp, R.H.
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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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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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Strong List Edge Coloring of Subcubic Graphs
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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Precise Upper Bound for the Strong Edge Chromatic Number of Sparse Planar Graphs
Discussiones Mathematicae Graph Theory, 2013 We prove that every planar graph with maximum degree ∆ is strong edge (2∆−1)-colorable if its girth is at least 40+1. The bound 2∆−1 is reached at any graph that has two adjacent vertices of degree ∆.
Borodin Oleg V., Ivanova Anna O.
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Strong edge-coloring for jellyfish graphs
Discrete Mathematics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gerard J. Chang +4 more
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