Daniel P. Johnston

activity

20232026

collaborators

6 papers

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…

math.CO2025

Isolation number: Cartesian and lexicographic products and generalized Sierpiński graphs

Bostjan Bresar, Tanja Dravec, Daniel P. Johnston +3

The isolation number $ι (G)$ of a graph $G$ is the minimum cardinality of a set $A \subset V (G)$ such that the subgraph induced by the vertices that are not in the union of the close…

math.CO2025

The Saturation Spectrum of Berge Stars

Neal Bushaw, Sean English, Emily Heath +2

The forbidden subgraph problem is among the oldest in extremal combinatorics -- how many edges can an $n$ -vertex $F$ -free graph have? The answer to this question is the well-studie…

math.CO2024

Isolation game on graphs

Boštjan Brešar, Tanja Dravec, Daniel P. Johnston +2

Given a graph $G$ and a family of graphs $F$ , an $F$ -isolating set, as introduced by Caro and Hansberg, is any set $S \subset V (G)$ such that $G - N [S]$ contains no member…

math.CO2023

Orientable total domination in graphs

Sarah E. Anderson, Tanja Dravec, Daniel Johnston +1

Given a directed graph $D$ , a set $S \subseteq V (D)$ is a total dominating set of $D$ if each vertex in $D$ has an in-neighbor in $S$ . The total domination number of $D$ , denoted $…