Results 231 to 240 of about 9,430 (262)

A generalization of edge‐coloring in graphs

Journal of Graph Theory, 1986
AbstractBounds are given on the number of colors required to color the edges of a graph (multigraph) such that each color appears at each vertex v at most m(ν) times. The known results and proofs generalize in natural ways. Certain new edge‐coloring problems, which have no counterparts when m(ν) = 1 for all ν ϵ V, are studied.
S. Louis Hakimi, Oded Kariv
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Edge‐colored saturated graphs

Journal of Graph Theory, 1987
AbstractA graph G is (k1, k2, …, kt)‐saturated if there exists a coloring C of the edges of G in t colors 1, 2, …, t in such a way that there is no monochromatic complete ki‐subgraph K of color i, 1 ⩽ i ⩽ t, but the addition of any new edge of color i, joining two nonadjacent vertices in G, with C, creates a monochromatic K of color i, 1 ⩽ i ⩽ t.
Denis Hanson, Bjarne Toft
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Soft Edge Coloring

2007
We consider the following channel assignment problem arising in wireless networks. We are given a graph G= (V, E), and the number of wireless cards C v for all v, which limit the number of colors that edges incident to vcan use. We also have the total number of channels C G available in the network.
Chadi Kari, Yoo Ah Kim, Seungjoon Lee, Alexander Russell, Minho Shin   +4 more
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Maximal Edge-Colorings of Graphs

Graphs and Combinatorics, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mariusz Meszka, Magdalena Tyniec
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Edge Colorings of Embedded Graphs

Graphs and Combinatorics, 2000
The authors give some conditions for a graph to be embeddable in a surface with Eulerian negative characteristic and to have as chromatic index the maximum degree of its vertices.
Yan, Zhongde, Zhao, Yue
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A bibliographic survey of edge‐colorings

Journal of Graph Theory, 1978
AbstractThis paper presents a bibliography on edge‐colorings of graphs which is as complete as possible to date. We introduce the papers by a brief discussion of the ideas involved.
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Graph Edge Coloring: A Survey

Graphs and Combinatorics, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yan Cao 0001, Guantao Chen, Guangming Jing, Michael Stiebitz, Bjarne Toft   +4 more
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PARALLEL EDGE COLORING APPROXIMATION

Parallel Processing Letters, 1996
Let G be a graph with n vertices and m edges and let its maximum degree be Δ. It is shown that a valid edge coloring of G using at most 2Δ−1 colors can be computed in O( log n log Δ) time using O(m+n) processors on a CREW PRAM. Based on this, for any constant c>1, a valid edge coloring for G using at most max([cΔ], Δ+1) colors can be computed in O(
Martin Fürer, Balaji Raghavachari
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Graph Edge Coloring and Extensions of Edge Colorings

This dissertation explores two main questions which may be framed in terms of graph edge-coloring. First, an assignment of $k$ colors to the edges of the complete bipartite graph $K_{n,n}$ corresponds to an assignment of $k$ symbols to the cells of an $n\times n$ array.
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Note on injective edge-coloring of graphs

Discrete Applied Mathematics, 2022
Zhengke Miao, Yimin Song, Gexin Yu
exaly