Geodesic
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

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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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     author = {S. L. Berlov},
     title = {Helly's property for $n$-cliques and the degree of a~graph},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     volume = {340},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_340_a0/}
}
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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/