𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A note on possible extensions of Negami's conjecture

✍ Scribed by Hlin?n�, Petr

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
239 KB
Volume
32
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

A graph H is a cover of a graph G, if there exists a mapping ϕ from V (H) onto V (G) such that for every vertex v of G, ϕ maps the neighbors of v in H bijectively onto the neighbors of ϕ(v) in G. Negami conjectured in 1987 that a connected graph has a finite planar cover if and only if it embeds in the projective plane. This conjecture is not completely solved yet, but partial results due to Archdeacon, Fellows, Negami, and the author are known. This article suggests another formulation of this conjecture that has a straightforward generalization to higher nonorientable surfaces, and provides some support for the generalized version.

📜 SIMILAR VOLUMES

On a conjecture of Thomassen and Toft
On a conjecture of Thomassen and Toft
✍ Kriesell, Matthias 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 183 KB 👁 1 views

This article is motivated by a conjecture of Thomassen and Toft on the number s 2 (G) of separating vertex sets of cardinality 2 and the number v 2 (G) of vertices of degree 2 in a graph G belonging to the class G of all 2-connected graphs without nonseparating induced cycles. Let G denote the numbe

On a conjecture of Aris: Proof and remar
On a conjecture of Aris: Proof and remarks
✍ Dan Luss; Neal R. Amundson 📂 Article 📅 1967 🏛 American Institute of Chemical Engineers 🌐 English ⚖ 428 KB 👁 1 views
Proof of a conjecture on cycles in a bip
Proof of a conjecture on cycles in a bipartite graph
✍ Wang, Hong 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 244 KB 👁 1 views

It was conjectured in [Wang, to appear in The Australasian Journal of Combinatorics] that, for each integer k ≥ 2, there exists . This conjecture is also verified for k = 2, 3 in [Wang, to appear; Wang, manuscript]. In this article, we prove this conjecture to be true if n ≥ 3k, i.e., M (k) ≤ 3k. W