Results 261 to 270 of about 641,529 (298)

The NP-Completeness of Edge-Coloring

SIAM Journal on Computing, 1981
We show that it is NP-complete to determine the chromatic index of an arbitrary graph. The problem remains NP-complete even for cubic graphs.
exaly   +3 more sources

The strong edge-coloring for graphs with small edge weight [PDF]

open access: yesDiscrete 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{dG(u)+dG(v)|e=uv∈E(G)}. We study graphs with edge weight at most 7. We show that 1) every graph with edge
Gexin Yu, Xiangqian Zhou, Lily Chen
exaly   +2 more sources

Extending an edge‐coloring

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.
Odile Marcotte, Paul D. Seymour
openaire   +1 more source

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
openaire   +1 more source

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   +4 more
openaire   +1 more source

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
openaire   +2 more sources

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