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Quasi‐carousel tournaments
Author(s) -
Nagami Coregliano Leonardo
Publication year - 2018
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.22205
Subject(s) - tournament , mathematics , combinatorics , transitive relation , vertex (graph theory) , isomorphism (crystallography) , infinity , discrete mathematics , graph , crystallography , mathematical analysis , chemistry , crystal structure
A tournament is called locally transitive if the outneighborhood and the inneighborhood of every vertex are transitive. Equivalently, a tournament is locally transitive if it avoids the tournaments W 4 and L 4 , which are the only tournaments up to isomorphism on four vertices containing a unique 3‐cycle. On the other hand, a sequence of tournaments ( T n ) n ∈ Nwith V ( T n ) = n is called almost balanced if all but o ( n ) vertices of T n have outdegree ( 1 / 2 + o ( 1 ) ) n . In the same spirit of quasi‐random properties, we present several characterizations of tournament sequences that are both almost balanced and asymptotically locally transitive in the sense that the density of W 4 and L 4 in T n goes to zero as n goes to infinity.