Results 11 to 20 of about 39,087 (298)
Complete edge-colored permutation graphs
Advances in Applied Mathematics, 2022 Nous introduisons le concept de graphes de permutation complets de couleur d'arête comme des graphes complets qui sont l'union bord-disjonction de graphes de permutation « classiques ». Nous montrons qu'un graphe G=(V,E) est un graphe de permutation complet de couleur de bord si et seulement si chaque sous-graphe monochromatique de G est un graphe de ...
Tom Hartmann +5 more
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European Journal of Combinatorics, 2010 The authors deal with the coloured version of the \(k\)-linked problem in edge-coloured multigraphs. A graph is \(k\)-linked (\(k\geq 1\)) if for each \(k\) pairs of vertices \(x_1,u_1,\dots, x_k,y_k\) there exist \(k\) pairwise vertex disjoint paths, one per each pair \((x_i, y_i)\) (\(i= 1,\dots,k\)).
J. M. Becu +3 more
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Properly colored subgraphs in edge-colored graphs [PDF]
, 2023 Properly colored cycles are closely related to directed cycles in directed graphs, and play an important role in molecular biology, transportation and communication, social sciences and other fields.
Han, Tingting
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Majority Edge-Colorings of Graphs
The Electronic Journal of Combinatorics, 2023 We propose the notion of a majority $k$-edge-coloring of a graph $G$, which is an edge-coloring of $G$ with $k$ colors such that, for every vertex $u$ of $G$, at most half the edges of $G$ incident with $u$ have the same color. We show the best possible results that every graph of minimum degree at least $2$ has a majority $4$-edge-coloring, and that ...
Felix Bock +5 more
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On Graphs with Proper Connection Number 2
Theory and Applications of Graphs, 2021 An edge-colored graph is properly connected if for every pair of vertices u and v there exists a properly colored uv-path (i.e. a uv-path in which no two consecutive edges have the same color). The proper connection number of a connected graph G, denoted
Jill Faudree +5 more
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More on the Rainbow Disconnection in Graphs
Discussiones Mathematicae Graph Theory, 2022 Let G be a nontrivial edge-colored connected graph. An edge-cut R of G is called a rainbow-cut if no two of its edges are colored the same. An edge-colored graph G is rainbow disconnected if for every two vertices u and v of G, there exists a u-v-rainbow-
Bai Xuqing +3 more
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On Edge Coloring Bipartite Graphs [PDF]
SIAM Journal on Computing, 1982 The present paper shows how to find a minimal edge coloring of a bipartite graph with E edges and V vertices in time $O(E\log V)$.
Richard Cole 0001, John E. Hopcroft
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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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Generation of colored graphs with isomorphism rejection [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2021 In the article we consider graphs whose vertices or edges are colored in a given number of colors — vertex and edge colorings. The study of colorings of graphs began in the middle of the 19th century, but the main attention is paid to proper ...
Razumovsky, Peter Vladimirovich +1 more
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Electronic Notes in Discrete Mathematics, 2008 Abstract A split graph is a graph whose vertex set admits a partition into a stable set and a clique. The chromatic indexes for some subsets of split graphs, such as split graphs with odd maximum degree and split-indifference graphs, are known. However, for the general class, the problem remains unsolved.
S. M. ALMEIDA +2 more
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