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On Kelley's intersection numbers


Authors: Fred Galvin and Karel Prikry
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
Published electronically: July 27, 2000
MathSciNet review: 1707516
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] B. Bollobás, Extremal Graph Theory, Acad. Press, 1978. MR 80a:05120
  • [2] D.H. Fremlin, Measure Algebras, in Handbook of Boolean Algebras, ed. J.D. Monk (with coop. of R. Bonnet), North-Holland Publ. Co., Amsterdam 1989, 878-980. MR 99l:611
  • [3] P.D. Johnson, Jr., About two definitions of the fractional chromatic number, Geombinatorics V (1996), 99-108. MR 96k:05063
  • [4] J.L. Kelley, Measures on Boolean algebras, Pac. J. of Math. 9 (1959), 1165-1177. MR 21:7286
  • [5] I. Leader, The fractional chromatic number of infinite graphs, J. of Graph Theory 20 (1995), 411-417. MR 96j:05042
  • [6] E.R. Scheinerman, private communication.
  • [7] E.R. Scheinerman, D.H. Ullman, Fractional Graph Theory, John Wiley & Sons, Inc. 1997. MR 98m:05001
  • [8] P.D. Johnson, Jr., More on the fractional chromatic number, Geombinatorics 9 (1999), 10-20. CMP 99:15
  • [9] F.H. Clarke and R.E. Jamison, Multicolorings, measures and games on graphs, Discrete Math. 14 (1976), 241-245. MR 52:10472

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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

DOI: https://doi.org/10.1090/S0002-9939-00-05561-1
Keywords: Boolean algebra, strictly positive measure, intersection number, weak intersection number, hypergraph, fractional chromatic number
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
Article copyright: © Copyright 2000 American Mathematical Society

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