Ramsey numbers of cubes versus cliques
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Fox_Ramsey numbers.pdf
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282.88 KB
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Checksum (MD5)
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Author(s)
Conlon, David
Fox, Jacob
Lee, Choongbum
Sudakov, Benny
Date Issued
November 2014
Journal
Combinatorica
Publisher
Springer-Verlag/Bolyai Society
Citation
Conlon, David, Jacob Fox, Choongbum Lee, and Benny Sudakov. “Ramsey Numbers of Cubes Versus Cliques.” Combinatorica (November 5, 2014).
Version
Original manuscript
Abstract
The cube graph Q[subscript n] is the skeleton of the n-dimensional cube. It is an n-regular graph on 2[superscript n] vertices. The Ramsey number r(Q[subscript n] ;K[subscript s]) is the minimum N such that every graph of order N contains the cube graph Q[subscript n] or an independent set of order s. In 1983, Burr and Erdős asked whether the simple lower bound r(Q[subscript n] ;K[subscript s] )≥(s−1)(2[superscript n] −1)+1 is tight for s fixed and n sufficiently large. We make progress on this problem, obtaining the first upper bound which is within a constant factor of the lower bound.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00493-014-3010-x
