Results 241 to 250 of about 14,669 (262)
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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.
Hanson, D., Toft, B.
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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.
Hanson, D., Toft, B.
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Journal of Graph Theory, 1990
AbstractWhen can a k‐edge‐coloring of a subgraph K of a graph G be extended to a k‐edge‐coloring of G? One necessary condition is that for all X ⊆ E(G) ‐ E(K), where μi(X) is the maximum cardinality of a subset of X whose union with the set of edges of K colored i is a matching.
Marcotte, O., Seymour, P. D.
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AbstractWhen can a k‐edge‐coloring of a subgraph K of a graph G be extended to a k‐edge‐coloring of G? One necessary condition is that for all X ⊆ E(G) ‐ E(K), where μi(X) is the maximum cardinality of a subset of X whose union with the set of edges of K colored i is a matching.
Marcotte, O., Seymour, P. D.
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Journal of Algorithms, 1996
Summary: Many combinatorial problems can be efficiently solved for partial \(k\)-trees (graphs of treewidth bounded by \(k\)). The edge-coloring problem is one of the well-known combinatorial problems for which no efficient algorithms were previously known, except a polynomial-time algorithm of very high complexity.
Zhou, Xiao +2 more
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Summary: Many combinatorial problems can be efficiently solved for partial \(k\)-trees (graphs of treewidth bounded by \(k\)). The edge-coloring problem is one of the well-known combinatorial problems for which no efficient algorithms were previously known, except a polynomial-time algorithm of very high complexity.
Zhou, Xiao +2 more
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Edge Coloring Series Parallel Graphs
Journal of Algorithms, 1995Abstract We present an algorithm for optimally edge coloring series parallel graphs. We give a linear time implementation, as well as a parallel implementation, of the algorithm that runs in O (log 3 n ) time using O ( n ) processors. The sequential implementation, which is optimal, improves the best-known algorithm. The parallel implementation of
Caspi, Yuval, Dekel, Eliezer
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Edge‐colorings avoiding rainbow stars
Journal of Graph Theory, 2017AbstractWe consider an extremal problem motivated by a article of Balogh [J. Balogh, A remark on the number of edge colorings of graphs, European Journal of Combinatorics 27, 2006, 565–573], who considered edge‐colorings of graphs avoiding fixed subgraphs with a prescribed coloring.
Carlos Hoppen +3 more
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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 +4 more
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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 +4 more
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1995
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. In this paper, we survey recent advances and results on the classical edge-coloring problem as well as the generalized edge-coloring problems, called the f-coloring and Φ ...
Shin-ichi Nakano +2 more
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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. In this paper, we survey recent advances and results on the classical edge-coloring problem as well as the generalized edge-coloring problems, called the f-coloring and Φ ...
Shin-ichi Nakano +2 more
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Edge Colorings of Embedded Graphs
Graphs and Combinatorics, 2000The 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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