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Deterministic Distributed Edge-Coloring via Hypergraph Maximal Matching [PDF]
IEEE Annual Symposium on Foundations of Computer Science, 2017 We present a deterministic distributed algorithm that computes a (2δ-1)-edge-coloring, or even list-edge-coloring, in any n-node graph with maximum degree δ, in O(log^8 δ ⋅ log n) rounds.
Manuela Fischer, M. Ghaffari, F. Kuhn
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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 ...
Bock, Felix +5 more
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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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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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The strong edge-coloring for graphs with small edge weight
Discrete Mathematics, 2020 A strong edge-coloring of a graph G = ( V , E ) is a partition of its edge set E into induced matchings. The edge weight of a graph G is defined to be max { d G ( u ) + d G ( v ) | e = u v ∈ E ( G ) } . We study graphs with edge weight at most 7. We show
Lily Chen +3 more
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The Complexity of Distributed Edge Coloring with Small Palettes [PDF]
ACM-SIAM Symposium on Discrete Algorithms, 2017 The complexity of distributed edge coloring depends heavily on the palette size as a function of the maximum degree $\Delta$. In this paper we explore the complexity of edge coloring in the LOCAL model in different palette size regimes. 1.
Yi-Jun Chang +4 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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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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