F. Botler

collaborators

4 papers

math.CO2025

On Modular Edge Colourings of Graphs

GaÃ©tan Berthe, Marthe Bonamy, FÃ¡bio Botler +5

Given a graph $G$ and an integer $k \geq 2$ , let $I ¨ _{k}^{'} (G)$ denote the minimum number of colours required to colour the edges of $G$ such that, in each colour class, the subgraph in…

math.CO2025

Immersions of large cliques in graphs with independence number 2 and bounded maximum degree

FÃ¡bio Botler, Cristina G. Fernandes, Carla N. Lintzmayer +4

An immersion of a graph $H$ in a graph $G$ is a minimal subgraph $I$ of $G$ for which there is an injection $i : V (H) \to V (I)$ and a set of edge-disjoint paths $\{P_e:…

math.CO2025

Extremal Problems on Forest Cuts and Acyclic Neighborhoods in Sparse Graphs

F. Botler, Y. S. Couto, C. G. Fernandes +4

Chernyshev, Rauch, and Rautenbach proved that every connected graph on $n$ vertices with less than $\frac{11}{5} n - \frac{18}{5}$ edges has a vertex cut that induces a forest, and co…

math.CO2024

Ramsey Goodness of paths and unbalanced graphs

FÃ¡bio Botler, Luiz Moreira, JoÃ£o Pedro de Souza

Given graphs $G$ and $H$ , we say that $G$ is $H$ - $g oo d$ if the Ramsey number $R (G, H)$ equals the trivial lower bound $(∣ G ∣ - 1) (I ¨ (H) - 1) + I ¨ (H)$ , where $I ¨ (H)$ denotes the usual…