Results 41 to 50 of about 39,087 (298)
A decomposition of gallai multigraphs
Discussiones Mathematicae Graph Theory, 2014 An edge-colored cycle is rainbow if its edges are colored with distinct colors. A Gallai (multi)graph is a simple, complete, edge-colored (multi)graph lacking rainbow triangles.
Halperin Alexander +2 more
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Computing Minimum Rainbow and Strong Rainbow Colorings of Block Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 A path in an edge-colored graph $G$ is rainbow if no two edges of it are colored the same. The graph $G$ is rainbow-connected if there is a rainbow path between every pair of vertices.
Melissa Keranen, Juho Lauri
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Even edge colorings of a graph
Journal of Combinatorial Theory, Series B, 1985 It is shown that the minimum number of colors needed to paint the edges of a graph G so that in every cycle of G there is a nonzero even number of edges of at least one color is \(\lceil \log_ 2\chi (G)\rceil\), where \(\chi\) (G) denotes the vertex chromatic number of G, and \(\lceil \rceil\) denotes the least integer not less than the number inside ...
Noga Alon, Yoshimi Egawa
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Properly colored and rainbow cycles in edge-colored graphs [PDF]
, 2023 Graph coloring and the existence of cycles are two classic problems in graph theory, which are of great value in modeling and solving practical problems.
Wu, Fangfang
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Maximal edge colorings of graphs
European Journal of CombinatoricsFor a graph $G$ of order $n$ a maximal edge coloring is a proper edge coloring with $χ'(K_n)$ colors such that adding any edge to $G$ in any color makes it improper. Meszka and Tyniec proved that for some values of the number of edges there are no graphs with a maximal edge coloring, while for some other values, they provided constructions of such ...
Sebastian Babinski, Andrzej Grzesik
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On Monochromatic Subgraphs of Edge-Colored Complete Graphs
Discussiones Mathematicae Graph Theory, 2014 In a red-blue coloring of a nonempty graph, every edge is colored red or blue. If the resulting edge-colored graph contains a nonempty subgraph G without isolated vertices every edge of which is colored the same, then G is said to be monochromatic.
Andrews Eric +4 more
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Revisiting semistrong edge‐coloring of graphs
Journal of Graph Theory, 2023 AbstractA matching in a graph is semistrong if every edge of has an endvertex of degree one in the subgraph induced by the vertices of . A semistrong edge‐coloring of a graph is a proper edge‐coloring in which every color class induces a semistrong matching.
Borut Luzar +2 more
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On Mf-edge colorings of graphs.
Discuss. Math. Graph Theory, 2022 An edge coloring φ of a graph G is called an Mf-edge coloring if | φ(v)| ≤ f(v) for every vertex v of G, where φ(v) is the set of colors of edges incident with v and f is a function which assigns a positive integer f(v) to each vertex v. Let 𝒦f (G) denote the maximum number of colors used in an Mf-edge coloring of G.
Jaroslav Ivanco, Alfred Onderko
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Conflict-Free Connections of Graphs
Discussiones Mathematicae Graph Theory, 2018 An edge-colored graph G is conflict-free connected if any two of its vertices are connected by a path, which contains a color used on exactly one of its edges. In this paper the question for the smallest number of colors needed for a coloring of edges of
Czap Július +2 more
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Edge-Coloring Problems for Graphs.
Interdisciplinary Information Sciences, 1994 Summary: The edge-coloring problem is one of the fundamental problems on graphs, which often appears in various scheduling problems like the file transfer problem on computer networks. We survey old and new results on the classical edge-coloring problem as well as generalized edge-coloring problems, called the \(f\)-coloring and \(fg\)-coloring ...
NAKANO, Shin-ichi, NISHIZEKI, Takao
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