Number of Cliques in Graphs with a Forbidden Subdivision
Name
Lee-2015-Number of Cliques.pdf
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151.13 KB
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Author(s)
Lee, Choongbum
Oum, Sang-il
Date Issued
October 2015
Journal
SIAM Journal on Discrete Mathematics
Publisher
Society for Industrial and Applied Mathematics
Citation
Lee, Choongbum, and Sang-il Oum. “Number of Cliques in Graphs with a Forbidden Subdivision.” SIAM Journal on Discrete Mathematics 29, no. 4 (January 2015): 1999–2005. © 2015 Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
We prove that for all positive integers t, every n-vertex graph with no K[subscript t]-subdivision has at most 2[superscript 50t]n cliques. We also prove that asymptotically, such graphs contain at most 2[superscript (5+o(1))t]n cliques, where o(1) tends to zero as t tends to infinity. This strongly answers a question of Wood that asks whether the number of cliques in n-vertex graphs with no K[subscript t]-minor is at most 2[superscript ct]n for some constant c.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/140979988
