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
Full-text PDF Free Access
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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.
- Eric Babson and Dmitry N. Kozlov, Topological obstructions to graph colorings, Electron. Res. Announc. Amer. Math. Soc. 9 (2003), 61–68. MR 2029466, DOI https://doi.org/10.1090/S1079-6762-03-00112-4
BK03b E. Babson, D.N. Kozlov, Complexes of graph homomorphisms, Israel J. Math. 152 (2006), pp. 285–312.
BK03c E. Babson, D.N. Kozlov, Proof of the Lovász Conjecture, Annals of Mathematics (2), in press. arXiv:math.CO/0402395
IAS 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
Sch C. Schultz, A short proof of $w_1^n(\mathtt {Hom}(C_{2r+1}, K_{n+2}))=0$ for all $n$ and a graph colouring theorem by Babson and Kozlov, 8 pages, 2005. arXiv:math.AT/0507346
Sch3 C. Schultz, The relative strength of topological graph colouring obstructions, 10 pages, 2006.
BK03a E. Babson, D.N. Kozlov, Topological obstructions to graph colorings, Electron. Res. Announc. Amer. Math. Soc. 9 (2003), pp. 61–68.
BK03b E. Babson, D.N. Kozlov, Complexes of graph homomorphisms, Israel J. Math. 152 (2006), pp. 285–312.
BK03c E. Babson, D.N. Kozlov, Proof of the Lovász Conjecture, Annals of Mathematics (2), in press. arXiv:math.CO/0402395
IAS 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
Sch C. Schultz, A short proof of $w_1^n(\mathtt {Hom}(C_{2r+1}, K_{n+2}))=0$ for all $n$ and a graph colouring theorem by Babson and Kozlov, 8 pages, 2005. arXiv:math.AT/0507346
Sch3 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
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
