arXiv subjects

Jonatas Teodomiro

Publications and source records attributed to Jonatas Teodomiro.

3 recordsLinked to original sources

arXiv2026

Sharp Same-Color Cycle Covers in Two-Colored Complete Graphs

We extend the conjecture of Erdős and Gyárfás on monochromatic path covers to the setting of monochromatic cycle covers. We prove that, for all $n$, every 2-edge-coloring of the complete graph on $n$ vertices contains a collection of at most $\lceil\sqrt{n}\rceil$ monochromatic cycles, all of the same color, that together cover all vertices. The order of the bound is best possible, and the ceiling is necessary for infinitely many $n$.

math.CO↗

arXiv2026

Efficient Decomposition of Forman-Ricci Curvature on Vietoris-Rips Complexes and Data Applications

Discrete Forman-Ricci curvature (FRC) is an efficient tool that characterizes essential geometrical features and associated transitions of real-world networks, extending seamlessly to higher-dimensional computations in simplicial complexes. In this article, we provide two major advancements: First, we give a decomposition for FRC that inhently allows a local computations of FRC. Second, we construct a set-theoretical proof enabling an efficient algorithms for the local computation of FRC in Vietoris-Rips (VR) complexes. Our findings open new avenues for geometric computations in VR complexes and highlight an essential yet under-explored aspect of data analysis and visualisation: the geometry underpinning statistical patterns.

math.GT↗

arXiv2025

Alternative set-theoretical algorithms for efficient computations of cliques in Vietoris-Rips complexes

Identifying cliques in dense networks remains a formidable challenge, even with significant advances in computational power and methodologies. To tackle this, numerous algorithms have been developed to optimize time and memory usage, implemented across diverse programming languages. Yet, the inherent NP-completeness of the problem continues to hinder performance on large-scale networks, often resulting in memory leaks and slow computations. In the present study, we critically evaluate classic algorithms to pinpoint computational bottlenecks and introduce novel set-theoretical approaches tailored for network clique computation. Our proposed algorithms are rigorously implemented and benchmarked against existing Python-based solutions, demonstrating superior performance. These findings underscore the potential of set-theoretical techniques to drive substantial performance gains in network analysis.

math.CO↗