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Cobounding odd cycle colorings


Author: Dmitry N. Kozlov
Journal: Electron. Res. Announc. Amer. Math. Soc. 12 (2006), 53-55
MSC (2000): Primary 55M35; Secondary 05C15, 57S17
Published electronically: May 10, 2006
MathSciNet review: 2226524
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Abstract: We prove that the $ (n-2)$nd power of the Stiefel-Whitney class of the space of all $ n$-colorings of an odd cycle is 0 by presenting a cochain whose coboundary is the desired power of the class. This gives a very short self-contained combinatorial proof of a conjecture by Babson and the author.


References [Enhancements On Off] (What's this?)

  • 1. Eric Babson and Dmitry N. Kozlov, Topological obstructions to graph colorings, Electron. Res. Announc. Amer. Math. Soc. 9 (2003), 61–68 (electronic). MR 2029466, 10.1090/S1079-6762-03-00112-4
  • 2. E. Babson, D.N. Kozlov, Complexes of graph homomorphisms, Israel J. Math. 152 (2006), pp. 285-312.
  • 3. E. Babson, D.N. Kozlov, Proof of the Lovász Conjecture, Annals of Mathematics (2), in press. arXiv:math.CO/0402395
  • 4. D.N. Kozlov, Chromatic numbers, morphism complexes, and Stiefel-Whitney characteristic classes, in: Geometric Combinatorics, IAS/Park City Mathematics Series 14, in press. arXiv:math.AT/0505563
  • 5. C. Schultz, A short proof of $ w_1^n(\tt {Hom}\,(C_{2r+1}, K_{n+2}))=0$ for all $ n$ and a graph colouring theorem by Babson and Kozlov, 8 pages, 2005. arXiv:math.AT/0507346
  • 6. C. Schultz, The relative strength of topological graph colouring obstructions, 10 pages, 2006.

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Additional Information

Dmitry N. Kozlov
Affiliation: Institute of Theoretical Computer Science, ETH Zürich, Switzerland
Email: dkozlov@inf.ethz.ch

DOI: https://doi.org/10.1090/S1079-6762-06-00161-2
Received by editor(s): March 15, 2006
Published electronically: May 10, 2006
Additional Notes: Research supported by Swiss National Science Foundation Grant PP002-102738/1
Communicated by: Sergey Fomin
Article copyright: © Copyright 2006 American Mathematical Society