
TL;DR
This paper characterizes large classes of tournament families that are prevalent in large random tournaments, providing explicit constructions and identifying conditions under which families are dominant.
Contribution
It introduces the concept of dominant families of tournaments and characterizes several large such families for all sufficiently large h, including subgraph containment and feedback arc set size conditions.
Findings
Families containing large subgraphs are dominant for large h.
Families with bounded feedback arc set size are dominant.
Explicit constructions of dominant families for small h.
Abstract
For a tournament with vertices, its typical density is , i.e. this is the expected density of in a random tournament. A family of -vertex tournaments is {\em dominant} if for all sufficiently large , there exists an -vertex tournament such that the density of each element of in is larger than its typical density by a constant factor. Characterizing all dominant families is challenging already for small . Here we characterize several large dominant families for every . In particular, we prove the following for all sufficiently large: (i) For all tournaments with at least vertices, the family of all -vertex tournaments that contain as a subgraph is dominant. (ii) The family of all -vertex tournaments whose minimum feedback arc set size is at most…
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Taxonomy
TopicsGraph theory and applications · Limits and Structures in Graph Theory
