A 1-factor of a graph G = (V, E) is a collection of disjoint edges which contain all the vertices of V . Given a 2n -1 edge coloring of K2n, n ≥ 3, we prove there exists a 1-factor of K2n whose edges have distinct colors. Such a 1-factor is called a ''Rainbow.''
The existence of Ck-factorizations of K2n − F
✍ Scribed by D.G. Hoffman; P.J. Schellenberg
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 414 KB
- Volume
- 97
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
A necessary condition for the existence of a C,-factorization of KZn -F is that k divides 2n. It is known that neither K, -F nor K,, -F admit a C,-factorization.
In this paper we show that except for these two cases, the necessary condition is also sufficient.
📜 SIMILAR VOLUMES
## Abstract Let ${\cal F}$ be a 1‐factorization of the complete uniform hypergraph ${\cal G}={K\_{rn}^{(r)}}$ with $r \geq 2$ and $n\geq 3$. We show that there exists a 1‐factor of ${\cal G}$ whose edges belong to __n__ different 1‐factors in ${\cal F}$. Such a 1‐factor is called a “rainbow” 1‐fact
In a paper with the same title (Enomoto et al., 1985) we proved Chv&al's conjecture that ktough graphs have k-factors if they satisfy trivial necessary conditions. In this paper, we introduce a variation of toughness, and prove a stronger result for the existence of l-or 2-factors. This solves a con
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