Daniel P. Johnston

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20232026

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math.CO2026

Domination game and total domination game played on Sierpiński graphs

Tanja Dravec, Daniel P. Johnston, Sandi Klavžar

The game domination numbers $γ_{g}$ and $γ_{g}^{'}$ , and the game total domination numbers $γ_{tg}$ and $γ_{tg}^{'}$ are investigated on Sierpiński graphs $…

math.CO2026

On the Turán number of the directed path

Daniel P. Johnston, Cory Palmer, Amites Sarkar

In this note we determine the maximum number of arcs in a digraph on $n$ vertices that does not contain a length- $k$ directed path $P_{k + 1}$ for $n \geq 50 k^{6}$ . Th…