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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] H.-J. Bandelt, E. Prisner, “Clique graphs and Helly graphs”, J. Combin. Theory Ser. B, 51:1 (1991), 34–45 | DOI | MR | Zbl

[2] P. Erdös and T. Gallai, “On minimal number of vertices representing the edges of a graph”, Publ. Math. Inst. Hung. Acad. Sci, 6 (1961), 89–96 | MR

[3] A. Farrugia, Clique-Helly graphs and hereditary clique-Helly graphs, a mini-survey, Algoritmic graph theory(CS 762), Project, Dept. of Combinatorics, University of Waterloo, 2002

[4] R. Hamelink, “A partial characterization of clique graphs”, J. Combin. Theory, Ser. B, 5 (1968), 192–197 | DOI | MR | Zbl

[5] F. Roberts and J. Spencer, “Characterization of clique-graphs”, J. Combin. Theory, Ser. B, 10 (1971), 102–108 | DOI | MR | Zbl

[6] U. Tatt, Teoriya grafov, Mir, M., 1988 | MR