|
On Kelley's intersection numbers
Author(s):
Fred
Galvin;
Karel
Prikry
Journal:
Proc. Amer. Math. Soc.
129
(2001),
315-323.
MSC (2000):
Primary 06E10, 28A60
Posted:
July 27, 2000
MathSciNet review:
1707516
Retrieve article in:
PDF
This article is available free of charge
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:
-
- [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
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
06E10, 28A60
Retrieve articles in all Journals with
MSC (2000):
06E10, 28A60
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:
10.1090/S0002-9939-00-05561-1
PII:
S 0002-9939(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
Posted:
July 27, 2000
Additional Notes:
The first author's research was partially supported by NSF Grant DMS-9700796.
Communicated by:
Alan Dow
Copyright of article:
Copyright
2000,
American Mathematical Society
|
