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Some Recent Progress and Applications in Graph Minor Theory

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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.

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Authors and Affiliations

  1. The National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430

    Ken-ichi Kawarabayashi

  2. Department of Mathematics, Simon Fraser University, Burnaby, B.C, V5A 1S6

    Bojan Mohar

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  1. Ken-ichi Kawarabayashi
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  2. Bojan Mohar
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Correspondence to Ken-ichi Kawarabayashi.

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Research partly supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research, Grant number 16740044, by Sumitomo Foundation, by C & C Foundation and by Inoue Research Award for Young Scientists

Supported in part by the Research Grant P1–0297 and by the CRC program

On leave from: IMFM & FMF, Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia

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Kawarabayashi, Ki., Mohar, B. Some Recent Progress and Applications in Graph Minor Theory. Graphs and Combinatorics 23, 1–46 (2007). https://doi.org/10.1007/s00373-006-0684-x

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