On oriented 2-factorable graphs

On Deeply Critical Oriented Graphs

✍ O.V. Borodin; D. Fon-Der-Flaass; A.V. Kostochka; A. Raspaud; E. Sopena 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 96 KB

For every positive integer k, we present an oriented graph G k such that deleting any vertex of G k decreases its oriented chromatic number by at least k and deleting any arc decreases the oriented chromatic number of G k by two.

On the oriented chromatic index of orien

On the oriented chromatic index of oriented graphs

✍ Pascal Ochem; Alexandre Pinlou; Éric Sopena 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 227 KB

## Abstract A homomorphism from an oriented graph __G__ to an oriented graph __H__ is a mapping $\varphi$ from the set of vertices of __G__ to the set of vertices of __H__ such that $\buildrel {\longrightarrow}\over {\varphi (u) \varphi (v)}$ is an arc in __H__ whenever $\buildrel {\longrightarrow}

On Highly Factorable Numbers

✍ Jun Kyo Kim 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 287 KB

For a positive integer n, let f (n) be the number of multiplicative partions of n. We say that a nutural number n is highly factorable if f (m)< f (n) for all m, 1 ma j then f (np j Âp i ) f (n). Using this fact, we prove the conjecture of Canfield, Erdo s, and Pormerance: for each fixed k, if n is

A theorem on pancyclic-oriented graphs

✍ Maria Overbeck-Larisch 📂 Article 📅 1977 🏛 Elsevier Science 🌐 English ⚖ 275 KB

Pancyclic oriented graphs

✍ Zeng Min Song 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 324 KB

## Abstract Let __D__ be an oriented graph of order __n__ ≧ 9 and minimum degree __n__ − 2. This paper proves that __D__ is pancyclic if for any two vertices __u__ and __v__, either __uv__ ≅ __A(D)__, or __d__~__D__~^+^(__u__) + __d__~__D__~^−^(__v__) ≧ __n__ − 3.

On 2-factors of a bipartite graph

✍ Wang, Hong 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 191 KB 👁 2 views

In this article, we consider the following problem: Given a bipartite graph G and a positive integer k, when does G have a 2-factor with exactly k components? We will prove that if , then, for any bipartite graph H = (U 1 , U 2 ; F ) with |U 1 | ≤ n, |U 2 | ≤ n and ∆(H) ≤ 2, G contains a subgraph i