F. Botler

activity

20162022

most citedOn Gallai's and Hajós' Conjectures for graphs with treewidth at most 3

5 citations · 11 across the 6 of their papers we have counts for

collaborators

10 papers

math.CO2022

Seymour's Second Neighborhood Conjecture for orientations of (pseudo)random graphs

Fábio Botler, Phablo F. S. Moura, Tássio Naia

Seymour's Second Neighborhood Conjecture (SNC) states that every oriented graph contains a vertex whose second neighborhood is as large as its first neighborhood. We investigate th…

math.CO2021

Counting orientations of graphs with no strongly connected tournaments

Fábio Botler, Carlos Hoppen, Guilherme Oliveira Mota

Let $S_{k} (n)$ be the maximum number of orientations of an $n$ -vertex graph $G$ in which no copy of $K_{k}$ is strongly connected. For all integers $n$ , $k \geq 4$ where $n \geq 5$ or $k…

math.CO2020

Decomposition of $(2 k + 1)$ -regular graphs containing special spanning $2 k$ -regular Cayley graphs into paths of length $2 k + 1$

Fábio Botler, Luiz Hoffmann

A $P_{ℓ}$ -decomposition of a graph $G$ is a set of paths with $ℓ$ edges in $G$ that cover the edge set of $G$ . Favaron, Genest, and Kouider (2010) conjectured that every $(2k+1…

math.CO2020★ 1 cited

The mod $k$ chromatic index of graphs is $O (k)$

Fábio Botler, Lucas Colucci, Yoshiharu Kohayakawa

Let $χ_{k}^{'} (G)$ denote the minimum number of colors needed to color the edges of a graph $G$ in a way that the subgraph spanned by the edges of each color has all degrees congruent t…

math.CO2020★ 5 cited

Counting graph orientations with no directed triangles

Pedro Araújo, Fábio Botler, Guilherme Oliveira Mota

Alon and Yuster proved that the number of orientations of any $n$ -vertex graph in which every $K_{3}$ is transitively oriented is at most $2^{⌊ n^{2} /4 ⌋}$ for $n \geq 1 0^{4}$ …

math.CO2020

On Tuza's conjecture for triangulations and graphs with small treewidth

Fábio Botler, Cristina G. Fernandes, Juan Gutiérrez

Tuza (1981) conjectured that the size $τ (G)$ of a minimum set of edges that intersects every triangle of a graph $G$ is at most twice the size $ν (G)$ of a maximum set of edge-disjo…