We survey known results on the existence and enumeration of many kinds of 1-factorizations of the complete graph. We also mention briefly some related questions and topics, as well as applications.

One-factorizations of the complete graph—A survey

A degree factor of a graph is either an r-factor (regular of degree r) or an [m, n]-factor (with each degree between m and n). In a component factor, each component is a prescribed graph. Both kinds of factors are surveyed, and also corresponding factorizations.

Factors and factorizations of graphs—a survey

An isomorphic factorization of a graph is a decomposition into isomorphic edge-disjoint subgraphs. A number of new and old open problems on isomorphic factorizations are presented along with some existing related results.

Isomorphic factorizations X: Unsolved problems

On the Anderson-Lipman conjecture and some related problems

The edge chromatic number of G is the minimum number of colors required to color the edges of G in such a way that no two adjacent edges have the same color. We will determine a sufficient condition for a various graph products to be of class 1, namely, strong product, semistrong product, and special product.

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On the edge coloring of graph products

Let G[H] denote the composition of the graphs G and H. If G can be decomposed into one-factors and two-factors, H can be decomposed into one-factors, and H is not the empty graph on an odd number of vertices, then G[H] can be decomposed into one-factors.

P. Himelwright

Papers

On one-factorizations of compositions of graphs