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

DOI:
https://doi.org/10.1090/S1079-6762-06-00161-2

Published electronically:
May 10, 2006

MathSciNet review:
2226524

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the nd power of the Stiefel-Whitney 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 self-contained 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. MR**2029466**, https://doi.org/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 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:
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