C. Hoppen

collaborators

6 papers

math.CO2026

Separating path systems for cubic graphs and for complete bipartite graphs

Cristina Fernandes, Carlos Hoppen, George Kontogeorgiou +2

A strongly separating path system in a graph $G$ is a collection $P$ of paths in $G$ such that, for every two edges $e$ and $f$ of $G$ , there is a paths in $P$ …

math.CO2026

On the minimum number of eigenvalues of matrices associated with cographs

Luiz Emilio Allem, Martin FÃ¼rer, Carlos Hoppen +2

A symmetric matrix $M = (m_{ij}) \in R^{n \times n}$ is said to be associated with an $n$ -vertex graph $G = (V, E)$ with vertex set ${v_{1}, \dots, v_{n}}$ if, for every $i \neq j…

cs.SI2025

Multi-Community Spectral Clustering for Geometric Graphs

Luiz Emilio Allem, Konstantin Avrachenkov, Carlos Hoppen +2

In this paper, we consider the soft geometric block model (SGBM) with a fixed number $k \geq 2$ of homogeneous communities in the dense regime, and we introduce a spectral clusteri…

math.CO2025

The minimum number of distinct eigenvalues of a threshold graph is at most $4$

Luiz Emilio Allem, Carlos Hoppen, JoÃ£o Lazzarin +2

In this note we show that the minimum number of distinct eigenvalues of a threshold graph is at most $4$ . Moreover, given any threshold graph $G$ and any nonzero real number $I^»$ ,…

math.CO2025

Maximum number of edge colorings avoiding rainbow copies of $K_{4}$

HiÃªp HÃ n, Carlos Hoppen, Nicolas Moro MÃ¼ller +1

In this paper we show that for $r \geq 12$ and any sufficiently large $n$ -vertex graph $G$ the number of $r$ -edge-colorings of $G$ with no rainbow $K_{4}$ is at most $r^{e x (n, K_{4})}$ ,…

math.CO2025

On the minimum number of eigenvalues of trees of diameter seven

Luiz Emilio Allem, Carlos Hoppen, Lucas Siviero Sibemberg

The underlying graph $G$ of a symmetric matrix $M = (m_{ij}) \in R^{n \times n}$ is the graph with vertex set ${v_{1}, \dots, v_{n}}$ such that a pair ${v_{i}, v_{j}}$ with $i\neq j…

Separating path systems for cubic graphs and for complete bipartite graphs

On the minimum number of eigenvalues of matrices associated with cographs

Multi-Community Spectral Clustering for Geometric Graphs

The minimum number of distinct eigenvalues of a threshold graph is at most 4

Maximum number of edge colorings avoiding rainbow copies of K4​

On the minimum number of eigenvalues of trees of diameter seven

The minimum number of distinct eigenvalues of a threshold graph is at most $4$

Maximum number of edge colorings avoiding rainbow copies of $K_{4}$