Bovstjan Brevsar

activity

20172026

most citedGraphs with a unique maximum open packing

3 citations · 4 across the 13 of their papers we have counts for

collaborators

13 papers

math.CO2026

Smooth Graphs

Boštjan Brešar, Manoj Changat, Prasanth G. Narasimha-Shenoi +2

The notion of smoothness was introduced originally in the context of step systems on connected graphs. Smoothness turns out to be a very general property of metrics defined by a fi…

math.CO2026

Frugal coloring of graphs revisited

Boštjan Brešar, Wenjie Hu, Babak Samadi

Given a graph $G$ and a positive integer $t$ , an independent set $S \subseteq V (G)$ is $t$ -frugal if every vertex has at most $t$ neighbors in $S$ . A $t$ -frugal coloring of $G$ is a…

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

Injective (edge) colorings of generalized Sierpiński graphs

C. K. Bhanupriya, Boštjan Brešar

Generalized Sierpiński graphs constitute a distinctive class of fractal-like networks with recursive definition: given a graph $G$ , $S_{G}^{1} = G$ while $S_{G}^{n}$ is obtained from $|V(G)|…

math.CO2025

On $k$ -coalition in graphs: bounds and exact values

Boštjan Brešar, Michael A. Henning, Babak Samadi

Given a graph $G=\big{(}V(G),E(G)\big{)}$, a set $S \subseteq V (G)$ is called a $k$ -dominating set if every vertex in $V (G) ∖ S$ has at least $k$ neighbors in $S$ . Two disjoi…

math.CO2025

On polluted bootstrap percolation in Cartesian grids

Boštjan Brešar, Jaka Hedžet, Michael A. Henning

Given a graph $G$ and assuming that some vertices of $G$ are infected, the $r$ -neighbor bootstrap percolation rule makes an uninfected vertex $v$ infected if $v$ has at least $r$ i…

math.CO2024

Spreading in claw-free cubic graphs

Boštjan Brešar, Jaka Hedžet, Michael A. Henning

Let $p \in N$ and $q \in N \cup {\infty}$ . We study a dynamic coloring of the vertices of a graph $G$ that starts with an initial subset $S$ of blue…

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.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.CO2020★ 1 cited

Domination in digraphs and their products

Boštjan Brešar, Kirsti Kuenzel, Douglas F. Rall

A dominating (respectively, total dominating) set $S$ of a digraph $D$ is a set of vertices in $D$ such that the union of the closed (respectively, open) out-neighborhoods of verti…

math.CO2020

$S$ -packing colorings of distance graphs $G (Z, {2, t})$

Boštjan Brešar, Jasmina Ferme, Karolína Kamenická

Given a graph $G$ and a non-decreasing sequence $S = (a_{1}, a_{2}, \dots)$ of positive integers, the mapping $f : V (G) \to {1, \dots, k}$ is an $S$ -packing $k$ -coloring of $G$ if…

math.CO2019★ 3 cited

Graphs with a unique maximum open packing

Boštjan Brešar, Kirsti Kuenzel, Douglas F. Rall

A set $S$ of vertices in a graph is an open packing if (open) neighborhoods of any two distinct vertices in $S$ are disjoint. In this paper, we consider the graphs that have a uniq…

math.CO2017

Packing coloring of Sierpiński-type graphs

Boštjan Brešar, Jasmina Ferme

The packing chromatic number $χ_{ρ} (G)$ of a graph $G$ is the smallest integer $k$ such that the vertex set of $G$ can be partitioned into sets $V_{i}$ , $i \in {1, \dots, k}$ , where ea…

Smooth Graphs

Frugal coloring of graphs revisited

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

Injective (edge) colorings of generalized Sierpiński graphs

On k-coalition in graphs: bounds and exact values

On polluted bootstrap percolation in Cartesian grids

Spreading in claw-free cubic graphs

k-Domination invariants on Kneser graphs

On the dissociation number of Kneser graphs

Domination in digraphs and their products

S-packing colorings of distance graphs G(Z,{2,t})

Graphs with a unique maximum open packing

Packing coloring of Sierpiński-type graphs

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

On $k$ -coalition in graphs: bounds and exact values

$k$ -Domination invariants on Kneser graphs

$S$ -packing colorings of distance graphs $G (Z, {2, t})$