The current work, which further generalizes some of the above results, is again probabilistic, and uses, in addition to earlier ideas, connections with so-called {\em normal} distributions on the set of matchings of a graph. For fixed $k\geq 2$, ${\cal H}$ a $k$-bounded hypergraph, and $t:{\cal H}\rightarrow \mbox{{\bf R}}^+$ a fractional cover, a sufficient condition is given to ensure that the edge cover number $\rho({\cal H})$, {\em i.e.}, the size of a smallest set of edges of ${\cal H}$ with union $V({\cal H})$, is asymptotically at most $t({\cal H}) = \sum_{A\in {\cal H}}t(A)$. This settles a conjecture first publicized in Visegr\'{a}d, June 1991.
FOOTNOTE
The paper (and the dissertation upon which it is based) was written
while the author was a DIMACS-affiliated mathematics graduate student
of Jeff Kahn. Both the paper and the dissertation were written using
the DIMACS Sun terminal room. DIMACS was acknowledged in the author's
dissertation, which should now be in the Rutgers math library. It
seems appropriate to include the extended abstract in the DIMACS
technical report series as well.
Paper available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1995/95-55.ps.gz
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