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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.
Fendy Septyanto, Kiki A. Sugeng
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Strong Edge Coloring of Generalized Petersen Graphs [PDF]
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 ...
Ming Chen, Lianying Miao, Shan Zhou
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The strong 3-rainbow index of some certain graphs and its amalgamation [PDF]
Opuscula Mathematica, 2022 We introduce a strong \(k\)-rainbow index of graphs as modification of well-known \(k\)-rainbow index of graphs. A tree in an edge-colored connected graph \(G\), where adjacent edge may be colored the same, is a rainbow tree if all of its edges have ...
Zata Yumni Awanis, A.N.M. Salman
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Strong Edge Coloring of K4(t)-Minor Free Graphs
Axioms, 2023 A strong edge coloring of a graph G is a proper coloring of edges in G such that any two edges of distance at most 2 are colored with distinct colors. The strong chromatic index χs′(G) is the smallest integer l such that G admits a strong edge coloring ...
Huixin Yin, Miaomiao Han, Murong Xu
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Grünbaum colorings extended to non-facial 3-cycles
Electronic Journal of Graph Theory and Applications, 2022 We consider the question of when a triangulation with a Grünbaum coloring can be edge-colored with three colors such that the non-facial 3-cycles also receive all three colors; we will call this a strong Grünbaum coloring.
sarah-marie belcastro, Ruth Haas
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Strong Chromatic Index of Outerplanar Graphs
Axioms, 2022 The strong chromatic index χs′(G) of a graph G is the minimum number of colors needed in a proper edge-coloring so that every color class induces a matching in G. It was proved In 2013, that every outerplanar graph G with Δ≥3 has χs′(G)≤3Δ−3.
Ying Wang +3 more
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Exact square coloring of graphs resulting from some graph operations and products
AKCE International Journal of Graphs and Combinatorics, 2022 A vertex coloring of a graph [Formula: see text] is called an exact square coloring of G if any pair of vertices at distance 2 receive distinct colors.
Priyamvada, B. S. Panda
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The strong 3-rainbow index of edge-comb product of a path and a connected graph
Electronic Journal of Graph Theory and Applications, 2022 Let G be a connected and edge-colored graph of order n, where adjacent edges may be colored the same. A tree in G is a rainbow tree if all of its edges have distinct colors. Let k be an integer with 2 ≤ k ≤ n.
Zata Yumni Awanis +2 more
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Graphs with Strong Proper Connection Numbers and Large Cliques
Axioms, 2023 In this paper, we mainly investigate graphs with a small (strong) proper connection number and a large clique number. First, we discuss the (strong) proper connection number of a graph G of order n and ω(G)=n−i for 1⩽i⩽3. Next, we investigate the rainbow
Yingbin Ma, Xiaoxue Zhang, Yanfeng Xue
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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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