M. Claverol

activity

20052024

most citedTotal domination in plane triangulations

1 citations · 2 across the 9 of their papers we have counts for

collaborators

11 papers

cs.CG2024

Sibson's formula for higher order Voronoi diagrams

Mercè Claverol, Andrea de las Heras-Parrilla, Clemens Huemer +1

Let $S$ be a set of $n$ points in general position in $R^{d}$ . The order- $k$ Voronoi diagram of $S$ , $V_{k} (S)$ , is a subdivision of $R^{d}$ into cells whose points hav…

math.CO2023

On polynomials associated to Voronoi diagrams of point sets and crossing numbers

Mercè Claverol, Andrea de las Heras-Parrilla, David Flores-Peñaloza +2

Three polynomials are defined for given sets $S$ of $n$ points in general position in the plane: The Voronoi polynomial with coefficients the numbers of vertices of the order- $k$ V…

cs.CG2022

Voronoi Diagrams of Arbitrary Order on the Sphere

Mercè Claverol, Andrea de las Heras Parrilla, Clemens Huemer

For a given set of points $U$ on a sphere $S$ , the order $k$ spherical Voronoi diagram $S V_{k} (U)$ decomposes the surface of $S$ into regions whose points have the same $k$ nearest p…

math.CO2022

Paired and semipaired domination in triangulations

M. Claverol, C. Hernando, M. Maureso +2

A dominating set of a graph $G$ is a subset $D$ of vertices such that every vertex not in $D$ is adjacent to at least one vertex in $D$ . A dominating set $D$ is paired if the subgr…

math.CO2021

The edge labeling of higher order Voronoi diagrams

Mercè Claverol, Andrea de las Heras Parrilla, Clemens Huemer +1

We present an edge labeling of order- $k$ Voronoi diagrams, $V_{k} (S)$ , of point sets $S$ in the plane, and study properties of the regions defined by them. Among them, we show that $…

math.CO2020★ 1 cited

Total domination in plane triangulations

M. Claverol, A. García, G. Hernández +4

A total dominating set of a graph $G = (V, E)$ is a subset $D$ of $V$ such that every vertex in $V$ is adjacent to at least one vertex in $D$ . The total domination number of $G$ , deno…