92 research outputs found
Generalized Tur\'an problems for disjoint copies of graphs
Given two graphs and , the maximum possible number of copies of in
an -free graph on vertices is denoted by . We investigate the
function , where denotes vertex disjoint copies of a fixed
graph . Our results include cases when is a complete graph, cycle or a
complete bipartite graph.Comment: 18 pages. There was a wrong statement in the first version, it is
corrected no
An improvement of the general bound on the largest family of subsets avoiding a subposet
Let be the maximum size of a family of subsets of not containing as a (weak) subposet, and let be the length of
a longest chain in . The best known upper bound for in terms of
and is due to Chen and Li, who showed that for any fixed .
In this paper we show that for any fixed , improving the best known upper bound. By choosing appropriately, we
obtain that as a corollary, which we show is best
possible for general . We also give a different proof of this corollary by
using bounds for generalized diamonds. We also show that the Lubell function of
a family of subsets of not containing as an induced subposet is
for every .Comment: Corrected mistakes, improved the writing. Also added a result about
the Lubell function with forbidden induced subposets. The final publication
will be available at Springer via http://dx.doi.org/10.1007/s11083-016-9390-
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