Results 51 to 60 of about 1,425,497 (376)
On facial unique-maximum (edge-)coloring [PDF]
, 2017 A facial unique-maximum coloring of a plane graph is a vertex coloring where on each face $\alpha$ the maximal color appears exactly once on the vertices of $\alpha$.
Andova, Vesna +4 more
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Improved Bounds for Some Facially Constrained Colorings
Discussiones Mathematicae Graph Theory, 2023 A facial-parity edge-coloring of a 2-edge-connected plane graph is a facially-proper edge-coloring in which every face is incident with zero or an odd number of edges of each color. A facial-parity vertex-coloring of a 2-connected plane graph is a proper
Štorgel Kenny
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Edge-colorability of graph bundles
Journal of Combinatorial Theory, Series B, 1983 AbstractThe topological notion of a fibre bundle is a generalization both of a Cartesian product and of a covering space. A graph bundle is a combinatorial analog of a fibre bundle. Accordingly, it is a generalization both of a Cartesian product of two graphs and of a covering graph. A “total graph”X is formed from a “base graph”B and “fibre”F.
Pisanski, T. +2 more
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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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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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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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Mixed graph edge coloring [PDF]
Discrete Mathematics, 2009 AbstractWe are interested in coloring the edges of a mixed graph, i.e., a graph containing unoriented and oriented edges. This problem is related to a communication problem in job-shop scheduling systems. In this paper we give general bounds on the number of required colors and analyze the complexity status of this problem. In particular, we provide NP-
Furmańczyk, Hanna +3 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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Distributed Degree Splitting, Edge Coloring, and Orientations [PDF]
ACM-SIAM Symposium on Discrete Algorithms, 2016 We study a family of closely-related distributed graph problems, which we call degree splitting, where roughly speaking the objective is to partition (or orient) the edges such that each node's degree is split almost uniformly.
M. Ghaffari, Hsin-Hao Su
semanticscholar +1 more source