Tanja Dravec

activity

20212026

most citedGraphs with unique Grundy dominating sets

2 citations · 3 across the 13 of their papers we have counts for

collaborators

16 papers

math.CO2026

Domination and Total Domination in Johnson graphs

María Gracia Cornet, Tanja Dravec, Pablo Torres

In this paper we study domination and total domination of Johnson graphs $J (n, k)$ . We establish monotonicity results proving that both $γ (J (n, k))$ and $γ_{t} (J (n, k))$ are non-decreas…

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.CO2025

A proof of the $\frac{3}{8}$ -conjecture for independent domination in cubic graphs

Boštjan Brešar, Tanja Dravec, Michael A. Henning

A set $S$ of vertices in a graph $G$ is a dominating set of $G$ if every vertex not in $S$ is adjacent to a vertex in~ $S$ . An independent dominating set in $G$ is a dominating set…

math.CO2025

Monophonic number of Kneser graphs and strongly 2-monophonic graphs

Boštjan Brešar, María Gracia Cornet, Tanja Dravec

Given a graph $G$ a set $S \subset V (G)$ is called monophonic if every vertex in $G$ lies on some induced path between two vertices in $S$ . The monophonic number, $m (G)$ , of $G$ , wh…

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

Thresholds for the biased Maker-Breaker domination games

Boštjan Brešar, Csilla Bujtás, Pakanun Dokyeesun +1

In the $(a, b)$ -biased Maker-Breaker domination game, two players alternately select unplayed vertices in a graph $G$ such that Dominator selects $a$ and Staller selects $b$ vertice…

math.CO2024

Graphs with span 1 and shortest optimal walks

Tanja Dravec, Mirjana Mikalački, Andrej Taranenko

A span of a given graph $G$ is the maximum distance that two players can keep at all times while visiting all vertices (edges) of $G$ and moving according to certain rules, that pr…

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.CO2024

Maker-Breaker domination game critical graphs

Athira Divakaran, Tanja Dravec, Tijo James +2

The Maker-Breaker domination game (MBD game) is a two-player game played on a graph $G$ by Dominator and Staller. They alternately select unplayed vertices of $G$ . The goal of Domi…

math.CO2024★ 1 cited

Induced matching vs edge open packing: trees and product graphs

Bostjan Bresar, Tanja Dravec, Jaka Hedzet +1

Given a graph $G$ , the maximum size of an induced subgraph of $G$ each component of which is a star is called the edge open packing number, $ρ_{e}^{o} (G)$ , of $G$ . Similarly, the m…

math.CO2023

$k$ -Domination invariants on Kneser graphs

Boštjan Brešar, María Gracia Cornet, Tanja Dravec +1

In this follow-up to [M.G.~Cornet, P.~Torres, arXiv:2308.15603], where the $k$ -tuple domination number and the 2-packing number in Kneser graphs $K (n, r)$ were studied, we are conce…

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 $…

math.CO2023

Bounds on zero forcing using (upper) total domination and minimum degree

Boštjan Brešar, María Gracia Cornet, Tanja Dravec +1

While a number of bounds are known on the zero forcing number $Z (G)$ of a graph $G$ expressed in terms of the order of a graph and maximum or minimum degree, we present two bounds…

math.CO2023

Spreading in graphs

Boštjan Brešar, Tanja Dravec, Aysel Erey +1

Several concepts that model processes of spreading (of information, disease, objects, etc.) in graphs or networks have been studied. In many contexts, we assume that some vertices…

math.CO2021

On the dissociation number of Kneser graphs

Boštjan Brešar, Tanja Dravec

A set $D$ of vertices of a graph $G$ is a dissociation set if each vertex of $D$ has at most one neighbor in $D$ . The dissociation number of $G$ , $d i ss (G)$ , is the cardinality of a…

math.CO2021★ 2 cited

Graphs with unique Grundy dominating sets

Boštjan Brešar, Tanja Dravec

Given a graph $G$ consider a procedure of building a dominating set $D$ in $G$ by adding vertices to $D$ one at a time in such a way that whenever vertex $x$ is added to $D$ there…

Domination and Total Domination in Johnson graphs

Domination game and total domination game played on Sierpiński graphs

A proof of the 83​-conjecture for independent domination in cubic graphs

Monophonic number of Kneser graphs and strongly 2-monophonic graphs

Isolation number: Cartesian and lexicographic products and generalized Sierpiński graphs

Thresholds for the biased Maker-Breaker domination games

Graphs with span 1 and shortest optimal walks

Isolation game on graphs

Maker-Breaker domination game critical graphs

Induced matching vs edge open packing: trees and product graphs

k-Domination invariants on Kneser graphs

Orientable total domination in graphs

Bounds on zero forcing using (upper) total domination and minimum degree

Spreading in graphs

On the dissociation number of Kneser graphs

Graphs with unique Grundy dominating sets

A proof of the $\frac{3}{8}$ -conjecture for independent domination in cubic graphs

$k$ -Domination invariants on Kneser graphs