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Local conditions for exponentially many subdivisions

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Liu, Hong, Sharifzadeh, Maryam and Staden, Katherine (2017) Local conditions for exponentially many subdivisions. Combinatorics, Probability and Computing, 26 (3). pp. 423-430. doi:10.1017/S0963548316000365

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Official URL: https://doi.org/10.1017/S0963548316000365

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Abstract

Given a graph F, let st(F) be the number of subdivisions of F, each with a different vertex set, which one can guarantee in a graph G in which every edge lies in at least t copies of F. In 1990, Tuza asked for which graphs F and large t, one has that st(F) is exponential in a power of t. We show that, somewhat surprisingly, the only such F are complete graphs, and for every F which is not complete, st(F) is polynomial in t. Further, for a natural strengthening of the local condition above, we also characterize those F for which st(F) is exponential in a power of t.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Combinatorial analysis
Journal or Publication Title: Combinatorics, Probability and Computing
Publisher: Cambridge University Press
ISSN: 0963-5483
Official Date: May 2017
Dates:
DateEvent
May 2017Published
28 November 2016Available
7 November 2016Accepted
Volume: 26
Number: 3
Page Range: pp. 423-430
DOI: 10.1017/S0963548316000365
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: Engineering and Physical Sciences Research Council (EPSRC), Leverhulme Trust (LT), European Research Council (ERC)
Grant number: EP/K012045/1(EPSRC); 306493(ERC); ECF-2016-523(LT)

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