Chvátal's conjecture and point-intersections
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It is shown that among the maximal any-two-set-intersecting subsystems of a hereditary family F, there is a star, as claimed by a conjecture of Chvatal, if it is assumed that any two bases have at most one common element.
[1] Vašek Chvátal,et al. Intersecting families of edges in hypergraphs having the hereditary property , 1974 .
[2] Ping Wang,et al. Some results about the Chvátal conjecture , 1978, Discret. Math..