94 research outputs found
A hypergraph Tur\'an theorem via lagrangians of intersecting families
Let \mc{K}_{3,3}^3 be the 3-graph with 15 vertices and , and 11 edges ,
and . We show
that for large , the unique largest \mc{K}_{3,3}^3-free 3-graph on
vertices is a balanced blow-up of the complete 3-graph on 5 vertices. Our proof
uses the stability method and a result on lagrangians of intersecting families
that has independent interest
On the inducibility of cycles
In 1975 Pippenger and Golumbic proved that any graph on vertices admits
at most induced -cycles. This bound is larger by a
multiplicative factor of than the simple lower bound obtained by a blow-up
construction. Pippenger and Golumbic conjectured that the latter lower bound is
essentially tight. In the present paper we establish a better upper bound of
. This constitutes the first progress towards proving
the aforementioned conjecture since it was posed
Hamilton cycles in highly connected and expanding graphs
In this paper we prove a sufficient condition for the existence of a Hamilton
cycle, which is applicable to a wide variety of graphs, including relatively
sparse graphs. In contrast to previous criteria, ours is based on only two
properties: one requiring expansion of ``small'' sets, the other ensuring the
existence of an edge between any two disjoint ``large'' sets. We also discuss
applications in positional games, random graphs and extremal graph theory.Comment: 19 page
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