On the Number of 5‐Cycles in a Tournament | Zendy

Komarov Natasha | Zendy; Mackey John | Zendy

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On the Number of 5‐Cycles in a Tournament

Author(s) -

Komarov Natasha,

Mackey John

Publication year - 2017

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.22130

Subject(s) - tournament , mathematics , combinatorics , upper and lower bounds , enhanced data rates for gsm evolution , order (exchange) , discrete mathematics , computer science , mathematical analysis , economics , telecommunications , finance

We find a formula for the number of directed 5‐cycles in a tournament in terms of its edge scores and use the formula to find upper and lower bounds on the number of 5‐cycles in any n ‐tournament. In particular, we show that the maximum number of 5‐cycles is asymptotically equal to3 4n 5, the expected number 5‐cycles in a random tournament ( p = 1 2 ), with equality (up to order of magnitude) for almost all tournaments.

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