Balogh, József, Liu, Hong and Sharifzadeh, Maryam (2015) Subdivisions of a large clique in C6-free graphs. Journal of Combinatorial Theory, Series B, 112 . pp. 18-35. doi:10.1016/j.jctb.2014.11.004

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Abstract

Mader conjectured that every -free graph has a subdivision of a clique of order linear in its average degree. We show that every -free graph has such a subdivision of a large clique.

We also prove the dense case of Mader's conjecture in a stronger sense, i.e., for every c, there is a such that every -free graph with average degree has a subdivision of a clique with where every edge is subdivided exactly 3 times.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Graph theory, Combinatorial analysis
Journal or Publication Title:	Journal of Combinatorial Theory, Series B
Publisher:	Academic Press
ISSN:	0095-8956
Official Date:	May 2015
Dates:	Date Event May 2015 Published 22 November 2014 Available 22 November 2014 Accepted
Volume:	112
Page Range:	pp. 18-35
DOI:	10.1016/j.jctb.2014.11.004
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Description:	Open archive
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID UNSPECIFIED Simons Foundation http://dx.doi.org/10.13039/100000893 DMS-0745185 National Science Foundation http://dx.doi.org/10.13039/100000001 27763 Seventh Framework Programme http://dx.doi.org/10.13039/100011102 13039 Arnold and Mabel Beckman Foundation http://dx.doi.org/10.13039/100000997

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