A short proof of w_1^n(Hom(C_{2r+1}, K_{n+2}))=0 for all n and a graph colouring theorem by Babson and Kozlov

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dc.creatorSchultz, Carsten
dc.date2005-07-17
dc.date2006-06-30
dc.date.accessioned2026-07-07T06:42:38Z
dc.date.available2026-07-07T06:42:38Z
dc.descriptionWe show that the n-th power of the first Stiefel-Whitney class of the Z_2-operation on the graph complex Hom(C_{2r+1},K_{n+2})$ is zero, confirming a conjecture by Babson and Kozlov. This proves the strong form of their graph colouring theorem, which they had only proven for odd n. Our proof is also considerably simpler than their proof of the weak form of the theorem, which is also known as the Lovász conjecture.
dc.descriptionslight simplification of the proof, updated references
dc.identifierhttps://arxiv.org/abs/math/0507346
dc.identifierhttp://arxiv.org/abs/math/0507346
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/102114
dc.subjectAlgebraic Topology
dc.subjectCombinatorics
dc.subject57M15; 05C15
dc.titleA short proof of w_1^n(Hom(C_{2r+1}, K_{n+2}))=0 for all n and a graph colouring theorem by Babson and Kozlov
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