research-article

The Extremal Function for Complete Minors

Author:

Andrew ThomasonAuthors Info & Claims

Journal of Combinatorial Theory Series B, Volume 81, Issue 2

Pages 318 - 338

https://doi.org/10.1006/jctb.2000.2013

Published: 01 March 2001 Publication History

Abstract

Let c(t) be the minimum number c such that every graph G with e(G) c|G| contracts to a complete graph Kt. We show thatc(t)=( +o(1))tlogtwhere =0.319... is an explicit constant. Random graphs are extremal graphs.

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Chang YOshman RNolin AHalldorsson MBalliu A(2023)Efficient Distributed Decomposition and Routing Algorithms in Minor-Free Networks and Their ApplicationsProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594604(55-66)Online publication date: 19-Jun-2023
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Sau IStamoulis GThilikos D(2022)k-apices of Minor-closed Graph Classes. II. Parameterized AlgorithmsACM Transactions on Algorithms10.1145/351902818:3(1-30)Online publication date: 11-Oct-2022
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Index Terms

The Extremal Function for Complete Minors
1. Mathematics of computing
  1. Discrete mathematics
2. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image Journal of Combinatorial Theory Series B

Journal of Combinatorial Theory Series B Volume 81, Issue 2

March 2001

176 pages

ISSN:0095-8956

Editors:
Adrian Bondy
Univ. Claude Bernard Lyon I, Villeurbanne, France
,
U. S. R. Murty
Univ. of Waterloo, Waterloo, Ont., Canada

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Academic Press, Inc.

United States

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Published: 01 March 2001

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The extremal function for K₈^- minors