Bovstjan Brevsar

collaborators

7 papers

math.CO2026

Injective (edge) colorings of generalized SierpiÅski graphs

C. K. Bhanupriya, BoÅ¡tjan BreÅ¡ar

Generalized SierpiÅski 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.CO2026

Smooth Graphs

BoÅ¡tjan BreÅ¡ar, 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

BoÅ¡tjan BreÅ¡ar, 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

BoÅ¡tjan BreÅ¡ar, 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

Spreading in claw-free cubic graphs

BoÅ¡tjan BreÅ¡ar, Jaka HedÅ¾et, 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.CO2025

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

BoÅ¡tjan BreÅ¡ar, 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…

Injective (edge) colorings of generalized SierpiÅski graphs

Smooth Graphs

Frugal coloring of graphs revisited

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

Spreading in claw-free cubic graphs

On k-coalition in graphs: bounds and exact values

Injective (edge) colorings of generalized SierpiÅski graphs

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

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