Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part I, Tome 340 (2006), pp. 5-9
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S. L. Berlov. Helly's property for $n$-cliques and the degree of a graph. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part I, Tome 340 (2006), pp. 5-9. http://geodesic.mathdoc.fr/item/ZNSL_2006_340_a0/
@article{ZNSL_2006_340_a0,
author = {S. L. Berlov},
title = {Helly's property for $n$-cliques and the degree of a~graph},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {5--9},
year = {2006},
volume = {340},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_340_a0/}
}
TY - JOUR
AU - S. L. Berlov
TI - Helly's property for $n$-cliques and the degree of a graph
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2006
SP - 5
EP - 9
VL - 340
UR - http://geodesic.mathdoc.fr/item/ZNSL_2006_340_a0/
LA - ru
ID - ZNSL_2006_340_a0
ER -
%0 Journal Article
%A S. L. Berlov
%T Helly's property for $n$-cliques and the degree of a graph
%J Zapiski Nauchnykh Seminarov POMI
%D 2006
%P 5-9
%V 340
%U http://geodesic.mathdoc.fr/item/ZNSL_2006_340_a0/
%G ru
%F ZNSL_2006_340_a0
The following main result is proved. Let the maximal clique of a graph $G$ have $n$ vertices, and let the degree of any vertex of $G$ be less than $\lceil \frac{5}{3}n\rceil$. Consider a family of pairwise intersecting $n$-cliques. The the intersection of all cliques from that family has more than $n/3$ vertices. It is shown that the result is sharp.
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