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Injective edge-coloring of subcubic graphs
Discret. Math. Algorithms Appl., 2021An injective edge-coloring [Formula: see text] of a graph [Formula: see text] is an edge-coloring such that if [Formula: see text], [Formula: see text], and [Formula: see text] are three consecutive edges in [Formula: see text] (they are consecutive if ...
B. Ferdjallah +2 more
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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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Edge coloring of signed graphs
Discrete Applied Mathematics, 2020In this paper, we introduce edge coloring for signed graphs which is naturally corresponding to the vertex coloring of their signed line graphs. Let χ ± ′ ( G , σ ) denote the edge chromatic number of a signed graph ( G , σ ) .
Li Zhang +4 more
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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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Faster Vizing and Near-Vizing Edge Coloring Algorithms
ACM-SIAM Symposium on Discrete AlgorithmsVizing's celebrated theorem states that every simple graph with maximum degree $\Delta$ admits a $(\Delta+1)$ edge coloring which can be found in $O(m \cdot n)$ time on $n$-vertex $m$-edge graphs.
Sepehr Assadi
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Star edge-coloring of graphs with maximum degree four
Applied Mathematics and Computation, 2019The star chromatic index χ st ′ ( G ) of a graph G is the smallest integer k for which G has a proper k-edge-coloring without bichromatic paths or cycles of length four. In this paper, we prove that (1) if G is a graph with Δ = 4 , then χ st ′ ( G ) ≤ 14
Y. Wang, Yiqiao Wang, Weifan Wang
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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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Recent progress on strong edge-coloring of graphs
Discret. Math. Algorithms Appl., 2019A strong edge-coloring of a graph [Formula: see text] is a partition of its edge set [Formula: see text] into induced matchings. In this paper, we gave a short survey on recent results about strong edge-coloring of a graph.
Kecai Deng, Gexin Yu, Xiangqian Zhou
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