Author

Petra Melicharová

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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 Sep 2026

On $S$-packing total colorings

In this paper, we generalize the concept of packing total coloring by introducing a new concept called the $S$-packing total coloring. For a graph $G$ and a non-decreasing sequence $S=(a_1,a_2,\ldots)$ of positive integers, an $S$-packing total coloring of $G$ is a mapping $c: V(G)\cup E(G)\rightarrow \{1,2,\ldots\}$ s...

Jasmina Ferme, Jaka Hedžet, Petra Melicharová et al. · 0 citations