scholarly journals A Planarity Criterion for Graphs

2015 ◽  
Vol 29 (4) ◽  
pp. 2160-2165 ◽  
Author(s):  
Kosta Došen ◽  
Zoran Petrić
Keyword(s):  
Planarity Criterion

Framed 4-valent graph minor theory I: Introduction. A planarity criterion and linkless embeddability

2014 ◽  
Vol 23 (07) ◽  
pp. 1460002
Author(s):  
Vassily Olegovich Manturov
Keyword(s):  
Graph Theory ◽  
The Other ◽  
Graph Minor ◽  
Other Hand ◽  
Simple Class ◽  
Points Of View ◽  
General Graphs ◽  
Planarity Criterion

This paper is the first one in the sequence of papers about a simple class of framed 4-graphs; the goal of this paper is to collect some well-known results on planarity and to reformulate them in the language of minors. The goal of the whole sequence is to prove analogs of the Robertson–Seymour–Thomas theorems for framed 4-graphs: namely, we shall prove that many minor-closed properties are classified by finitely many excluded graphs. From many points of view, framed 4-graphs are easier to consider than general graphs; on the other hand, framed 4-graphs are closely related to many problems in graph theory.

A Simple Planarity Criterion

1975 ◽  
Vol 22 (2) ◽  
pp. 226-230 ◽  
Author(s):  
Bernd Knauer
Keyword(s):  
Planarity Criterion

scholarly journals A planarity criterion for cubic bipartite graphs

1998 ◽  
Vol 191 (1-3) ◽  
pp. 31-43
Author(s):  
T. Böhme ◽  
J. Harant ◽  
A. Pruchnewski ◽  
I. Schiermeyer
Keyword(s):  
Bipartite Graphs ◽  
Planarity Criterion

scholarly journals Framed 4-valent graph minor theory II: Special minors and new examples

2015 ◽  
Vol 24 (13) ◽  
pp. 1541004
Author(s):  
Vassily Olegovich Manturov
Keyword(s):  
Graph Minor ◽  
Planarity Criterion

In the present paper, we proceed with the study of framed 4-graph minor theory initiated in [V. O. Manturov, Framed 4-valent graph minor theory I: Intoduction planarity criterion, arxiv: 1402.1564v1 [Math.Co]] and justify the planarity theorem for arbitrary framed 4-graphs; besides, we prove analogous results for embeddability in [Formula: see text].

scholarly journals A new proof of Vassiliev's conjecture

2014 ◽  
Vol 23 (07) ◽  
pp. 1460005 ◽  
Author(s):  
Igor Nikonov
Keyword(s):  
Finite Type ◽  
Opposite Edge ◽  
Edge Structure ◽  
First Order ◽  
Finite Type Invariants ◽  
Planarity Criterion

In the paper [First-order invariants and cohomology of spaces of embeddings of self-intersecting curves in ℝn, Izv. Math. 69(5) (2005) 865–912] on finite type invariants of self-intersecting curves, Vassiliev conjectured a criterion of planarity of framed four-valent graphs, i.e. 4-graphs with an opposite edge structure at each vertex. The conjecture was proved by Manturov [A proof of Vassilievs conjecture on the planarity of singular links, Izv. Math. 69(5) (2005) 169–178]. We give here another proof of Vassiliev's planarity criterion of framed four-valent graphs (and more generally, (even) *-graphs), which is based on Pontryagin–Kuratowski theorem.

Sign in / Sign up

Export Citation Format

Share Document