Reductions of $n$-fold covers
HTML articles powered by AMS MathViewer
- by Saul Stahl PDF
- Proc. Amer. Math. Soc. 72 (1978), 422-424 Request permission
Abstract:
Motivated by L. Lovász’s recent proof of the Kneser conjecture [3], this paper offers another result which relates topological and graph theoretical concepts. A method for converting n-fold covers to $(n - 1)$-fold covers is presented. This yields a strengthening of the classical Borsuk, Lusternik and Schnirelmann theorem on covers of spheres. The same conversion also has applications to multicolorings of graphs.References
-
K. Borsuk, Drei Sätze über die n-dimensionale euklidische Sphäre, Fund. Math. 20 (1933), 177-190.
- David Gale, Neighboring vertices on a convex polyhedron, Linear inequalities and related systems, Annals of Mathematics Studies, no. 38, Princeton University Press, Princeton, N.J., 1956, pp. 255–263. MR 0085552 L. Lovász, Kneser’s conjecture, homotopy and Borsuk’s theorem, J. Combinatorial Theory Ser. B (to appear). L. Lusternik and L. Schnirelmann, Méthodes topologiques dans les problèmes variationnels, Gosudarstvennoe Izdat., Moscow, 1930; rev. French transl., Actualités Sci. Indust., no. 118, Hermann, Paris, 1934.
- Saul Stahl, $n$-tuple colorings and associated graphs, J. Combinatorial Theory Ser. B 20 (1976), no. 2, 185–203. MR 406850, DOI 10.1016/0095-8956(76)90010-1
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 72 (1978), 422-424
- MSC: Primary 05A05; Secondary 05B40, 05C15
- DOI: https://doi.org/10.1090/S0002-9939-1978-0507351-9
- MathSciNet review: 507351