✦ LIBER ✦

Toughness and the existence of k-factors

✍ Scribed by Hikoe Enomoto; Bill Jackson; P. Katerinis; Akira Saito

Publisher: John Wiley and Sons
Year: 1985
Tongue: English
Weight: 317 KB
Volume: 9
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190090106

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

A degree condition for the existence of

A degree condition for the existence of k-factors

✍ Tsuyoshi Nishimura 📂 Article 📅 1992 🏛 John Wiley and Sons 🌐 English ⚖ 358 KB 👁 1 views

## Abstract Let __k__ be an integer such that ≦, and let __G__ be a connected graph of order __n__ with ≦, __kn__ even, and minimum degree at least __k__. We prove that if __G__ satisfies max(deg(u), deg(v)) ≦ n/2 for each pair of nonadjacent vertices __u, v__ in __G__, then __G__ has a __k__‐facto

On the existence of a rainbow 1-factor i

On the existence of a rainbow 1-factor in 1-factorizations of K

✍ S.I. El-Zanati; M.J. Plantholt; P.A. Sissokho; L.E. Spence 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 85 KB 👁 1 views

## 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

On the existence of rainbows in 1-factor

On the existence of rainbows in 1-factorizations of K2n

✍ David E. Woolbright; Hung-Lin FU 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 745 KB

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.''

Edge-chromatic critical graphs and the e

Edge-chromatic critical graphs and the existence of 1-factors

✍ S. A. Choudum 📂 Article 📅 1993 🏛 John Wiley and Sons 🌐 English ⚖ 300 KB 👁 1 views

## Abstract We give examples of edge‐chromatic critical graphs __G__ of the following types: (i) of even order and having no 1‐factor, and (ii) of odd order and having a vertex __v__ of minimum degree such that __G__ − __v__ has no 1‐factor. The first disproves a conjecture of S. Fiorini and R. J.

Some conditions for the existence of f-f

Some conditions for the existence of f-factors

✍ P. Katerinis 📂 Article 📅 1985 🏛 John Wiley and Sons 🌐 English ⚖ 268 KB 👁 1 views

Let m, 1, n be three odd integers such that m < I < n. It is proved that if a graph G has an mfactor and an rrfactor, then it also has an /factor. In addition, we obtain sufficient conditions for the existence of an f-factor, in terms of vertexdeleted subgraphs. All graphs considered here are multi

Forbidden subgraphs and the existence of

Forbidden subgraphs and the existence of a 2-factor

✍ R. E. L. Aldred; Jun Fujisawa; Akira Saito 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 195 KB 👁 1 views

## Abstract In this paper, we consider forbidden subgraphs which force the existence of a 2‐factor. Let \documentclass{article}\footskip=0pc\pagestyle{empty}\begin{document}${\cal G}$\end{document} be the class of connected graphs of minimum degree at least two and maximum degree at least three, an