Results 31 to 40 of about 9,430 (262)
Acyclicity in edge-colored graphs
Discrete Mathematics, 2017 A walk $W$ in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in $W$ is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type $i$ is a proper superset of graphs of acyclicity of type $i+1$, $i=1,2,3,4.$ The first three types are ...
Gregory Z. Gutin +4 more
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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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Degenerate matchings and edge colorings [PDF]
Discrete Applied Mathematics, 2018 A matching $M$ in a graph $G$ is $r$-degenerate if the subgraph of $G$ induced by the set of vertices incident with an edge in $M$ is $r$-degenerate. Goddard, Hedetniemi, Hedetniemi, and Laskar (Generalized subgraph-restricted matchings in graphs, Discrete Mathematics 293 (2005) 129-138) introduced the notion of acyclic matchings, which coincide with ...
Baste, Julien, Rautenbach, Dieter
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On the Star Chromatic Index of Generalized Petersen Graphs
Discussiones Mathematicae Graph Theory, 2021 The star k-edge-coloring of graph G is a proper edge coloring using k colors such that no path or cycle of length four is bichromatic. The minimum number k for which G admits a star k-edge-coloring is called the star chromatic index of G, denoted by χ′s (
Zhu Enqiang, Shao Zehui
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Edge-Coloring Bipartite Graphs [PDF]
Journal of Algorithms, 2000 This note provides an algorithm for finding \(\Delta\)(colors)-edge-coloring of a bipartite graph of order \(n\) and size \(m\) in time \(T+O(m\log \Delta)\) where \(T\) is the time needed to find a perfect matching in a \(k\)-regular bipartite graph, \(k\leq \Delta\), and \(\Delta\) is the maximum degree of vertices.
Ajai Kapoor, Romeo Rizzi
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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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Normal 5-edge-colorings of a family of Loupekhine snarks
AKCE International Journal of Graphs and Combinatorics, 2020 In a proper edge-coloring of a cubic graph an edge uv is called poor or rich, if the set of colors of the edges incident to u and v contains exactly three or five colors, respectively.
Luca Ferrarini +2 more
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M_{2}-edge colorings of dense graphs [PDF]
Opuscula Mathematica, 2016 An edge coloring \(\varphi\) of a graph \(G\) is called an \(\mathrm{M}_i\)-edge coloring if \(|\varphi(v)|\leq i\) for every vertex \(v\) of \(G\), where \(\varphi(v)\) is the set of colors of edges incident with \(v\).
Jaroslav Ivančo
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A note on M_{2}-edge colorings of graphs [PDF]
Opuscula Mathematica, 2015 An edge coloring \(\varphi\) of a graph \(G\) is called an \(M_2\)-edge coloring if \(|\varphi(v)|\le2 \) for every vertex \(v\) of \(G\), where \(\varphi(v)\) is the set of colors of edges incident with \(v\). Let \(K_2(G)\) denote the maximum number of
Július Czap
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On the Adjacent Strong Equitable Edge Coloring of Pn ∨ Pn, Pn ∨ Cn and Cn ∨ Cn
MATEC Web of Conferences, 2016 A proper edge coloring of graph G is called equitable adjacent strong edge coloring if colored sets from every two adjacent vertices incident edge are different,and the number of edges in any two color classes differ by at most one,which the required ...
Liu Jun +4 more
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