Sergey Savchenko

most citedOn 5-cycles and strong 5-subtournaments in a tournament of odd order n

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math.CO2024★ 1 cited

On 5-cycles and strong 5-subtournaments in a tournament of odd order n

Sergey Savchenko

Let $T$ be a tournament of odd order $n \geq 5,$ $c_{m} (T)$ be the number of its $m$ -cycles, and $s_{m} (T)$ be the number of its strongly connected $m$ -subtournaments. Due to work of…

math.CO2024

On the number of 8-cycles for two particular regular tournaments of order N with diametrically opposite local properties

Sergey Savchenko

For a regular tournament $T$ of order $n,$ denote by $c_{8} (T)$ the number of cycles of length $8$ in $T .$ Let $D R_{n}$ be a doubly-regular tournament of order $n \equiv 3 mod 4$ (so…

math.CO2023

Moon-type theorems on circuits in strongly connected tournaments of order $N$ and diameter $D$

Sergey Savchenko

Let $T$ be a strongly connected tournament of order $n \geq 4$ whose diameter does not exceed $d \geq 3.$ Denote by $c_{ℓ} (T)$ the number of circuits of length $ℓ$ in $T .$ In our…

On 5-cycles and strong 5-subtournaments in a tournament of odd order n

On the number of 8-cycles for two particular regular tournaments of order N with diametrically opposite local properties

Moon-type theorems on circuits in strongly connected tournaments of order N and diameter D

Moon-type theorems on circuits in strongly connected tournaments of order $N$ and diameter $D$