On Kelley’s intersection numbers
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- by Fred Galvin and Karel Prikry PDF
- Proc. Amer. Math. Soc. 129 (2001), 315-323 Request permission
Abstract:
We introduce a notion of weak intersection number of a collection of sets, modifying the notion of intersection number due to J.L. Kelley, and obtain an analogue of Kelley’s characterization of Boolean algebras which support a finitely additive strictly positive measure. We also consider graph-theoretic reformulations of the notions of intersection number and weak intersection number.References
- Béla Bollobás, Extremal graph theory, London Mathematical Society Monographs, vol. 11, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1978. MR 506522
- Lawrence M. Graves, The Weierstrass condition for multiple integral variation problems, Duke Math. J. 5 (1939), 656–660. MR 99
- P. D. Johnson Jr., About two definitions of the fractional chromatic number, Geombinatorics 5 (1996), no. 3, 99–108. MR 1367186
- J. L. Kelley, Measures on Boolean algebras, Pacific J. Math. 9 (1959), 1165–1177. MR 108570, DOI 10.2140/pjm.1959.9.1165
- Hermann Kober, Transformationen von algebraischem Typ, Ann. of Math. (2) 40 (1939), 549–559 (German). MR 96, DOI 10.2307/1968939
- E.R. Scheinerman, private communication.
- Edward R. Scheinerman and Daniel H. Ullman, Fractional graph theory, Wiley-Interscience Series in Discrete Mathematics and Optimization, John Wiley & Sons, Inc., New York, 1997. A rational approach to the theory of graphs; With a foreword by Claude Berge; A Wiley-Interscience Publication. MR 1481157
- P.D. Johnson, Jr., More on the fractional chromatic number, Geombinatorics 9 (1999), 10–20.
- F. H. Clarke and R. E. Jamison, Multicolorings, measures and games on graphs, Discrete Math. 14 (1976), no. 3, 241–245. MR 389641, DOI 10.1016/0012-365X(76)90036-4
Additional Information
- Fred Galvin
- Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
- Email: galvin@math.ukans.edu
- Karel Prikry
- Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
- Email: prikry@math.umn.edu
- Received by editor(s): July 7, 1998
- Received by editor(s) in revised form: April 15, 1999
- Published electronically: July 27, 2000
- Additional Notes: The first author’s research was partially supported by NSF Grant DMS-9700796.
- Communicated by: Alan Dow
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 315-323
- MSC (2000): Primary 06E10, 28A60
- DOI: https://doi.org/10.1090/S0002-9939-00-05561-1
- MathSciNet review: 1707516