Showing papers on "Edge coloring published in 1979"
TL;DR: In this article, a new graph coloring algorithm is presented and compared to a wide variety of known algorithms, which is shown to exhibit O(n 2) time behavior for most sparse graphs and thus is particularly well suited for use with large-scale scheduling problems.
Abstract: A new graph coloring algorithm is presented and compared to a wide variety of known algorithms. The algorithm is shown to exhibit O(n 2) time behavior for most sparse graphs and thus is found to be particularly well suited for use with large-scale scheduling problems. In addition, a procedure for generating large random test graphs with known chromatic number is presented and is used to evaluate heuristically the capabilities of the algorithms discussed.
537 citations
TL;DR: The graph Kn contains a cycle of length n with adjacent lines having different colors, and each point lies on more than 1 7 (5n+8) lines of different colors.
52 citations
TL;DR: A simple worst-case O(V) algorithm for determining a minimum edge coloring of an arbitrary bipartite graph with ‘v” vertices is presented.
13 citations
TL;DR: In this article, it was shown that if the size of the largest clique of a graph is small, or if the girth of the graph is large, then the bound x(G) 5 A (G) of Brooks Theorem can be improved considerably.
Abstract: A clique is necessarily a component of a graph G, and if A(G) = 2, then odd cycles are components. We refer to such components as Brooks components in order to use a collective name. First, we shall consider extensions of THEOREM 1 in which one color class has a certain property, i.e., it is a maximum independent set, or its vertices all have degree A(G). Then we give related results of Dirac [9] in which degc(o) h for all but a few exceptional vertices, and yet G still has an h-coloring. Finally, we present results which assert that if the size of the largest clique of G is small, or if the girth of G is large, then the bound x(G) 5 A(G) of Brooks’ Theorem can be improved considerably.
2 citations
TL;DR: The factorization and edge-coloring problems of the hypergraph Krxmh are studied, which is the complete, regular, h-uniform, r-partite hypergraph with m vertices in each of the r classes of vertices.
TL;DR: It is proved that if G is connected and has minimum degree 2, it is always possible unless b or w is 1 to coloring without isolates, and that the necessary knapsack inequality of (3) is, in most cases, sufficient.
TL;DR: It is proved among other results that every 2-edge-connected graph is F 8, as well as other results known for planar graphs through the use of the F k property.
TL;DR: Existence of some generalized edge colorings is proved by using the properties of hypergraphs as well as alternating chain methods.
Abstract: Existence of some generalized edge colorings is proved by using the properties of hypergraphs as well as alternating chain methods. A general framework is given for edge colorings and some general properties of balancing are derived.