Author

Marko Jakovac

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Preprint Sep 2026

A variety of the mutual-visibility coloring problem for graphs

This paper explores variations of vertex-coloring problems defined on graph visibility properties. It introduces and studies the dual, outer, and total mutual-visibility chromatic numbers, which partition the vertex set of a graph into color classes that preserve specific mutual-visibility conditions called dual, outer...

Saneesh Babu, Marko Jakovac, D. Kuziak et al. · 0 citations

Preprint Sep 2026

Settling the total domination-annihilation conjecture for graphs with minimum degree two

The total domination number $\gamma_t(G)$ of a graph $G$ is the minimum cardinality of a set $D\subseteq V(G)$ such that every vertex of $G$ has a neighbor in $D$. The annihilation number $a(G)$ is the largest integer $k$ for which the sum of the $k$ smallest degrees of $G$ is at most $|E(G)|$. A well-known conjecture,...

Marko Jakovac · 0 citations

Preprint Sep 2026

Sequence b-colorings in graphs

We introduce and begin the study of sequence b-colorings, a natural generalization of the classical notion of b-colorings introduced by Irving and Manlove in 1999. In a sequence b-coloring, each color class is required to contain a prescribed minimum number of color-dominating vertices (CDVs). We establish several fund...

Marko Jakovac, Michael S. Lang · 0 citations