NDLI: Cycles in Oriented 3-Graphs

Content Provider	Springer Nature Link
Author	Tan, Ta Sheng Leader, Imre
Copyright Year	2015
Abstract	An oriented 3-graph consists of a family of triples (3-sets), each of which is given one of its two possible cyclic orientations. A cycle in an oriented 3-graph is a positive sum of some of the triples that gives weight zero to each 2-set. Our aim in this paper is to consider the following question: how large can the girth of an oriented 3-graph be? We show that there exist oriented 3-graphs whose shortest cycle has length $$\frac{n^2}{2}(1+o(1))$$ : this is asymptotically best possible. We also show that there exist 3-tournaments whose shortest cycle has length $$\frac{n^2}{3}(1+o(1))$$ , in complete contrast to the case of 2-tournaments.
Ending Page	443
Page Count	12
Starting Page	432
File Format	PDF
ISSN	01795376
e-ISSN	14320444
Journal	Discrete & Computational Geometry
Issue Number	2
Volume Number	54
Language	English
Publisher	Springer US
Publisher Date	2015-05-30
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Cycles Computational Mathematics and Numerical Analysis Projective planes Tournaments Directed graphs (digraphs), tournaments Oriented graphs Combinatorics Paths and cycles
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Theoretical Computer Science Computational Theory and Mathematics Geometry and Topology

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Cycles in Oriented 3-Graphs