F. Botler

activity

20152025

most citedSeparating the edges of a graph by a linear number of paths

9 citations · 33 across the 19 of their papers we have counts for

collaborators

Showing 2020Show all

4 papers · 1 filter

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…

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

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

Counting graph orientations with no directed triangles

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

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

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