Fábio Botler

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math.CO2024

Separating the edges of a graph by cycles and by subdivisions of $K_{4}$

Fábio Botler, Tássio Naia

A separating system of a graph $G$ is a family $S$ of subgraphs of $G$ for which the following holds: for all distinct edges $e$ and $f$ of $G$ , there exists an element i…

math.CO2023

On the structure of a smallest counterexample and a new class verifying the 2-Decomposition Conjecture

F. Botler, A. Jiménez, M. Sambinelli +1

The 2-Decomposition Conjecture, equivalent to the 3-Decomposition Conjecture stated in 2011 by Hoffmann-Ostenhof, claims that every connected graph $G$ with vertices of degree 2 an…

math.CO2023

On nonrepetitive colorings of paths and cycles

Fábio Botler, Wanderson Lomenha, João Pedro de Souza

We say that a sequence $a_{1} \dots a_{2 t}$ of integers is repetitive if $a_{i} = a_{i + t}$ for every $i \in {1, \dots, t}$ . A walk in a graph $G$ is a sequence $v_{1} \dots v_{r}$ of vert…

math.CO2023

Independent dominating sets in planar triangulations

Fábio Botler, Cristina G. Fernandes, Juan Gutiérrez

In 1996, Matheson and Tarjan proved that every near planar triangulation on $n$ vertices contains a dominating set of size at most $n /3$ , and conjectured that this upper bound can…

Separating the edges of a graph by cycles and by subdivisions of K4​

On the structure of a smallest counterexample and a new class verifying the 2-Decomposition Conjecture

On nonrepetitive colorings of paths and cycles

Independent dominating sets in planar triangulations

Separating the edges of a graph by cycles and by subdivisions of $K_{4}$