Special Issue: 2013 TAPU Workshop on Knot Theory and Related TopicsNo Access

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

Vassily Olegovich Manturov

Bauman Moscow State Technical University, 2nd Baumanskaya St. 5/1, Moscow 105005, Russia

Laboratory of Quantum Topology, Chelyabinsk State University, Brat'ev Kashirinykh Street 129, Chelyabinsk 454001, Russia

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https://doi.org/10.1142/S0218216514600025Cited by:2 (Source: Crossref)

Abstract

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.

Keywords:

AMSC: 05C83, 57M25, 57M27

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