Cobounding odd cycle colorings
Author:
Dmitry N. Kozlov
Journal:
Electron. Res. Announc. Amer. Math. Soc. 12 (2006), 5355
MSC (2000):
Primary 55M35; Secondary 05C15, 57S17
Published electronically:
May 10, 2006
MathSciNet review:
2226524
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: We prove that the nd power of the StiefelWhitney class of the space of all 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 selfcontained combinatorial proof of a conjecture by Babson and the author.
 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
(2004i:05044), http://dx.doi.org/10.1090/S1079676203001124
 2.
E. Babson, D.N. Kozlov, Complexes of graph homomorphisms, Israel J. Math. 152 (2006), pp. 285312.
 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 StiefelWhitney characteristic classes, in: Geometric Combinatorics, IAS/Park City Mathematics Series 14, in press. arXiv:math.AT/0505563
 5.
C. Schultz, A short proof of for all 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.
 1.
 E. Babson, D.N. Kozlov, Topological obstructions to graph colorings, Electron. Res. Announc. Amer. Math. Soc. 9 (2003), pp. 6168. MR 2029466 (2004i:05044)
 2.
 E. Babson, D.N. Kozlov, Complexes of graph homomorphisms, Israel J. Math. 152 (2006), pp. 285312.
 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 StiefelWhitney characteristic classes, in: Geometric Combinatorics, IAS/Park City Mathematics Series 14, in press. arXiv:math.AT/0505563
 5.
 C. Schultz, A short proof of for all 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:
http://dx.doi.org/10.1090/S1079676206001612
PII:
S 10796762(06)001612
Received by editor(s):
March 15, 2006
Published electronically:
May 10, 2006
Additional Notes:
Research supported by Swiss National Science Foundation Grant PP002102738/1
Communicated by:
Sergey Fomin
Article copyright:
© Copyright 2006
American Mathematical Society
