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Enumeration of indecomposable tournaments with minimum Slater index
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The Slater index of a tournament is the minimum number of arcs that must be reversed in that tournament to make it a total order. Let [Formula: see text] be an integer with [Formula: see text]. The minimum value of the Slater index over the indecomposable [Formula: see text]-vertex tournaments is [Formula: see text]. In a recent paper [H. Belkhechine, C. Ben Salha, R. Romdhane, Indecomposable tournaments with minimum Slater index, Adv. Pure Appl. Math. 17 (2026) 60–77], we characterized the indecomposable [Formula: see text]-vertex tournaments with at least five vertices and minimum Slater index, i.e., with Slater index [Formula: see text]. In this paper, we asymptotically enumerate these tournaments.
World Scientific Pub Co Pte Ltd
Title: Enumeration of indecomposable tournaments with minimum Slater index
Description:
The Slater index of a tournament is the minimum number of arcs that must be reversed in that tournament to make it a total order.
Let [Formula: see text] be an integer with [Formula: see text].
The minimum value of the Slater index over the indecomposable [Formula: see text]-vertex tournaments is [Formula: see text].
In a recent paper [H.
Belkhechine, C.
Ben Salha, R.
Romdhane, Indecomposable tournaments with minimum Slater index, Adv.
Pure Appl.
Math.
17 (2026) 60–77], we characterized the indecomposable [Formula: see text]-vertex tournaments with at least five vertices and minimum Slater index, i.
e.
, with Slater index [Formula: see text].
In this paper, we asymptotically enumerate these tournaments.
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