Author

B. Brešar

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Preprint Oct 2026

Frugal coloring in planar graphs with maximum degree 4 and 5

A proper coloring of vertices of a graph $G$ is called $t$-frugal if no color appears more than $t$ times in the neighborhood of any vertex of $G$. While $1$-frugal coloring coincides with $2$-distance coloring, we study $2$-frugal colorings of planar graphs with maximum degree $4$ and $5$, respectively. We prove that...

B. Brešar, Přemysl Holub, Marko Jakovac et al. · 0 citations

Preprint Oct 2026

Partitioning an $S$-packing coloring into broadcast dominating sets

Given a graph $G$ and a positive integer $k$, a packing $k$-domatic coloring of $G$ is a function $f: V(G) \to \{1,\ldots,t\}$ such that (1) for any color $j \in \{1,\ldots, t\}$ and any two distinct vertices $u,v\in V(G)$ with $f(u)=f(v)=j$ we have $d_G(u,v)>j$, and (2) $V(G)$ admits a partition into $k$ sets $A_1,\ld...

B. Brešar, Jasmina Ferme, Wen-Jie Hu · 0 citations