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graph; neighbor; neighborhood hypergraph; clique hypergraph

References:

[3] Berge C., Duchet P.: **A generalization of Gilmore's theorem**. Recent Advances in Graph Theory, (Fiedler M., ed.), Academia, Prague, 1975, pp.49-55. MR 0406801 | Zbl 0325.05125

[4] Erdös P., Gallai T., Tuze Z.: **Covering the cliques of a graph with vertices**. Discrete Math. 108 (1992), 279-289. MR 1189850

[5] Jensen T.R., Toft B.: **Graph Coloring Problems**. Wiley Interscience, New York, 1995. MR 1304254 | Zbl 0855.05054

[6] Prisner E.: **Intersection multigraphs of uniform hypergraphs**. Graphs Combin. 14 (1998), 4 363-375. MR 1658849 | Zbl 0910.05048