Abstract
AbstractLet H be a 3-uniform hypergraph of order n with clique number $$\omega (H)=k$$
ω
(
H
)
=
k
. Assume that the union of the k-cliques of H equals its vertex set, the intersection of all maximum cliques of H is empty, but the intersection of all but one k-clique is non-empty. For fixed $$m=n-k$$
m
=
n
-
k
, Szemerédi and Petruska conjectured the sharp bound $$n\hbox {\,\,\char 054\,\,}{m+2\atopwithdelims ()2}$$
n
6
m
+
2
2
. In this note the conjecture is verified for $$m=2,3$$
m
=
2
,
3
and 4.
Funder
ELKH Alfréd Rényi Institute of Mathematics
Publisher
Springer Science and Business Media LLC
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