Convex independence and the structure of clone-free multipartite tournaments | Zendy

Darren B. Parker | Zendy; Randy F. Westhoff | Zendy; Marty J. Wolf | Zendy

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Convex independence and the structure of clone-free multipartite tournaments

Author(s) -

Darren B. Parker,

Randy F. Westhoff,

Marty J. Wolf

Publication year - 2009

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.1432

Subject(s) - mathematics , multipartite , combinatorics , regular polygon , independence (probability theory) , clone (java method) , independence number , tournament , discrete mathematics , graph , statistics , geometry , quantum , gene , physics , quantum mechanics , quantum entanglement , biochemistry , chemistry

We investigate the convex invariants associated with two-path convexity in clone-free multipartite tournaments. Specically , we explore the relationship between the Helly number, Radon number and rank of such digraphs. The main result is a structural theorem that describes the arc relationships among certain vertices associated with vertices of a given convexly independent set. We use this to prove that the Helly number, Radon number, and rank coincide in any clone-free bipartite tournament. We then study the relationship between Helly independence and Radon independence in clone-free multipartite tournaments. We show that if the rank is at least 4 or the Helly number is at least 3, then the Helly number and the Radon number are equal.

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