Some Recent Progress and Applications in Graph Minor Theory

Authors:
Ken-Ichi Kawarabayashi;Bojan Mohar
Affiliations:
The National Institute of Informatics, 2-1-2 Hitotsubashi, 101-8430, Tokyo, Chiyoda-ku;Simon Fraser University, 2-1-2 Hitotsubashi, V5A 1S6, Burnaby, B.C
Venue:
Graphs and Combinatorics
Year:
2007

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Abstract

In the core of the seminal Graph Minor Theory of Robertson and Seymour lies a powerful theorem capturing the ``rough'' structure of graphs excluding a fixed minor. This result was used to prove Wagner's Conjecture that finite graphs are well-quasi-ordered under the graph minor relation. Recently, a number of beautiful results that use this structural result have appeared. Some of these along with some other recent advances on graph minors are surveyed.