Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring

46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05) ◽

10.1109/sfcs.2005.14 ◽

2005 ◽

Cited By ~ 49

Author(s):

E.D. Demaine ◽

M.T. Hajiaghayi ◽

K.-i. Kawarabayashi

Keyword(s):

Graph Minor

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Graph minor

10.33915/etd.2122 ◽

2004 ◽

Author(s):

Jianbing Niu

Keyword(s):

Graph Minor

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Towards the Graph Minor Theorems for Directed Graphs

Automata, Languages, and Programming - Lecture Notes in Computer Science ◽

10.1007/978-3-662-47666-6_1 ◽

2015 ◽

pp. 3-10

Author(s):

Ken-Ichi Kawarabayashi ◽

Stephan Kreutzer

Keyword(s):

Directed Graphs ◽

Graph Minor

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

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216514600025 ◽

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.

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