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Author

Juan Gutiérrez

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Preprint Oct 2026

Dynamic Coloring and Graph Squares of Regular Graphs

An $r$-dynamic coloring of a graph $G$ is a proper vertex coloring in which every vertex $v$ sees at least $\min\{r,d(v)\}$ distinct colors in its neighborhood. The minimum number of colors in such a coloring is the $r$-dynamic chromatic number $\chi_r^d(G)$. We study dynamic colorings of regular graphs. A straighforwa...

Juan Gutiérrez, Grover Ugarte · 0 citations
Open access Jul 2026

On r-dynamic coloring of graphs in subclasses of planar and circulant graphs

An r-dynamic coloring of a graph G is a proper vertex coloring in which each vertex sees at least min{r, d(v)} distinct colors in its neighborhood. The minimum number of colors in such a coloring is the r-dynamic chromatic number χdr(G). We determine exact values and upper bounds of χdr for several graph classes, inclu...

Juan Gutiérrez, Grover Ugarte · 0 citations

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