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Extremal density for sparse minors and subdivisions

Abstract:

We prove an asymptotically tight bound on the extremal density guaranteeing subdivisions of bounded-degree bipartite graphs with a mild separability condition. As corollaries, we answer several questions of Reed and Wood on embedding sparse minors. Among others,
(1+o(1))t2 average degree is sufficient to force the t×t grid as a topological minor;
(3/2+o(1))t average degree forces every t-vertex planar graph as a minor, and the constant 3/2 is optimal, furthermore, surprisingly, the...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1093/imrn/rnab154

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Oxford University Press Publisher's website
Journal:
International Mathematics Research Notices Journal website
Publication date:
2021-06-30
Acceptance date:
2021-05-16
DOI:
EISSN:
1687-0247
ISSN:
1073-7928
Language:
English
Keywords:
Pubs id:
1224099
Local pid:
pubs:1224099
Deposit date:
2021-12-13

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