Electronic Only Electronic Research Announcements
Electronic Research Announcements
ISSN 1079-6762
Previous volume | Table of contents | Next volume
Articles in press | Most recent volume | All volumes
Previous Article | Next Article
 
Currently published by the American Institute of Mathematical Sciences as Electronic Research Announcements in Mathematical Sciences
 

Cobounding odd cycle colorings

Author(s): Dmitry N. Kozlov
Journal: Electron. Res. Announc. Amer. Math. Soc. 12 (2006), 53-55.
MSC (2000): Primary 55M35; Secondary 05C15, 57S17
Posted: May 10, 2006
Retrieve article in: PDF DVI PostScript

Abstract | References | Similar articles | Additional information

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:

1.
E. Babson, D.N. Kozlov, Topological obstructions to graph colorings, Electron. Res. Announc. Amer. Math. Soc. 9 (2003), pp. 61-68. MR 2029466 (2004i:05044)

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.

Similar Articles:

Retrieve articles in Electronic Research Announcements with MSC (2000): 55M35, 05C15, 57S17

Retrieve articles in all Journals with MSC (2000): 55M35, 05C15, 57S17

Additional Information:

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

DOI: 10.1090/S1079-6762-06-00161-2
PII: S 1079-6762(06)00161-2
Received by editor(s): March 15, 2006
Posted: May 10, 2006
Additional Notes: Research supported by Swiss National Science Foundation Grant PP002-102738/1
Communicated by: Sergey Fomin
Copyright of article: Copyright 2006, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google