FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 4, PAGES 1209-1226

Theorems of Helly--Gallai's type

V. L. Dol'nikov
S. A. Igonin

Abstract

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In this paper different generalizations of Helly's theorem for families of sets defined by systems of equations are presented. We investigate the existence problem of a $k$-element set, which has non-empty intersection with any member of such family. Applications to combinatorics and combinatorial geometry are given.

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Last modified: December 9, 1999