Crossing families

B. Aronov, P. Erdos, W. Goddard, D. J. Kleitman, M. Klugerman, J. Pach, L. J. Schulman

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Given a set of points in the plane, a crossing family is a collection of line segments, each joining two of the points, such that any two line segments intersect internally. Two sets A and B of points in the plane are mutually avoiding if no line subtended by a pair of points in A intersects the convex hull of B, and vice versa. We show that any set of n points in general position contains a pair of mutually avoiding subsets each of size at least {Mathematical expression}. As a consequence we show that such a set possesses a crossing family of size at least {Mathematical expression}, and describe a fast algorithm for finding such a family.

    Original languageEnglish (US)
    Pages (from-to)127-134
    Number of pages8
    JournalCombinatorica
    Volume14
    Issue number2
    DOIs
    StatePublished - Jun 1994

    Keywords

    • AMS subject classification code (1991): 52C10, 68Q20

    ASJC Scopus subject areas

    • Discrete Mathematics and Combinatorics
    • Computational Mathematics

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