https://hdl.handle.net/20.500.12008/48532 2026-08-10T05:13:48Z https://hdl.handle.net/20.500.12008/56289 Título: Skeleton of locally most separable 3-terminal graphs Autor: Würth, Simon; Romero, Pablo Resumen: A 3-terminal graph is a graph with 3 distinguished vertices, called terminals. Let Tn,m be the set of all connected 3-terminal graphs on n vertices and m edges. Let G be in Tn,m. A spanning subgraph H of G is 3-separable when H has precisely 3 components, each containing one terminal. For each p in [0, 1], the separability of G at p, denoted SG(p), is the probability that the resulting subgraph of G is 3-separable after each edge in G is removed independently with probability 1−p. The graph G is a locally most separable 3-terminal graph (LMS3TG) if for each H in Tn,m there exists δ > 0 such that SG(p) ≥ SH(p) whenever p ∈ (1 − δ, 1). Let Cn,m be the set of all connected simple graphs on n vertices and m edges. For each G in Cn,m, the skeleton G′ of G is the graph arising from G by the contraction of each of its bridges. In this note, we show that the skeleton of each LMS3TG in Tn,m is an almost-complete graph. Descripción: Documento elaborado en el marco de la pasantía de Investigación de PEDECIBA - Informática.; Orientador: Pablo Romero. 2026-01-01T00:00:00Z https://hdl.handle.net/20.500.12008/56235 Título: Grafos uniformemente más confiables y grafos fuertes Autor: Cabrera, Agustín Resumen: Sea Cn,m la clase de grafos conexos y simples con n vértices y m aristas. El co-rango de Cn,m y de cada uno de sus grafos es igual a m − n + 1. Sea G en Cn,m. Para cada ρ en [0, 1], se define la confiabilidad de G en ρ como la probabilidad de que el subgrafo obtenido de remover cada arista de G independientemente con probabilidad ρ sea conexo. Decimos que G es uniformemente más confiable si para cada H en Cn,m y cada ρ en [0, 1] se cumple que RG(ρ) ≥ RH(ρ). Decimos que un corte de G es un subconjunto de aristas U de G que cumple que G − U no es conexo. El número de cortes de G con k elementos se denota µk(G). Decimos que G es fuerte si para cada H en Cn,m y cada k en {0, . . . , m} se cumple que µk(G) ≤ µk(H). Es cierto que todo grafo fuerte es uniformemente más confiable. Boesch [J. Graph Theory 10 (1986), 339–352] conjeturó que todo grafo uniforme más confiable es fuerte. Se sabe que en cada una de las clases Cn,m cuyo co-rango es 4 o menor existe al menos un grafo uniformemente más confiable, y además cada grafo uniformemente más confiable es fuerte. Si bien existen infinitas clases Cn,m cuyo co-rango es igual a 5, se demostró recientemente que hay tan solo una cantidad finita de dichas clases que tienen un grafo que es uniformemente más confiable. Un proyecto ambicioso consiste en buscar una clase Cn,m que posea un grafo uniformemente más confiable que no sea fuerte. Dicha clase, en caso de existir, refutaría a la conjetura de Boesch. En este proyecto se realiza un estudio computacional relativo a la existencia o inexistencia de grafos uniformemente más confiables y de grafos fuertes dentro de clases Cn,m de co-rango 5. Descripción: Módulo de Taller de Ingeniería en Computación.; Orientador: Pablo Romero. 2026-01-01T00:00:00Z https://hdl.handle.net/20.500.12008/56052 Título: RETUYT-INCO at BEA 2026 Shared Task 2: meta-prompting in Rubric-based Scoring for German Autor: Sastre, Ignacio; Remersaro, Ignacio; Díaz, Facundo; de Horta, Nicolás; Chiruzzo, Luis; Rosá, Aiala; Góngora, Santiago Resumen: In this paper, we present the RETUYT-INCO participation at the BEA 2026 shared task “Rubric-based Short Answer Scoring for German”. Our team participated in track 1 (Unseen answers three-way), track 3 (Unseen answers two-way) and track 4 (Unseen questions two-way). Since these tracks required scoring short student answers using specific rubrics, we looked for ways to handle the changing nature of the task. We created a method called Metaprompting. In this approach, an LLM creates a custom prompt based on examples from the Train set. This prompt is then used to grade new student answers. Along with this method, we also describe other approaches we used, such as classic machine learning, fine-tuning open-source LLMs, and different prompting techniques. According to the official results, our team placed 6th out of 8 participants in Track 1 with a QWK of 0.729. In Track 3, we secured 4th place out of 9 with a QWK of 0.674, and we also placed 4th out of 8 in Track 4 with a QWK of 0.49. 2026-01-01T00:00:00Z https://hdl.handle.net/20.500.12008/55915 Título: RETUYT-INCO at BEA 2025 Shared Task: How Far Can Lightweight Models Go in AI-powered Tutor Evaluation? Autor: Góngora, Santiago; Sastre, Ignacio; Robaina, Santiago; Remersaro, Ignacio; Chiruzzo, Luis; Rosá, Aiala Resumen: In this paper, we present the RETUYT-INCO participation at the BEA 2025 shared task. Our participation was characterized by the decision of using relatively small models, with fewer than 1B parameters. This self-imposed restriction tries to represent the conditions in which many research groups or institutions are in the Global South, where computational power is not easily accessible due to its prohibitive cost. Even under this restrictive self-imposed setting, our models managed to stay competitive with the rest of teams that participated in the shared task. According to the exact F1 scores published by the organizers, our models had the following distances with respect to the winners: 6.46 in Track 1; 10.24 in Track 2; 7.85 in Track 3; 9.56 in Track 4; and 13.13 in Track 5. Considering that the minimum difference with a winner team is 6.46 points — and the maximum difference is 13.13 — according to the exact F1 score, we find that models with a size smaller than 1B parameters are competitive for these tasks, all of which can be run on computers with a low-budget GPU or even without a GPU. 2025-01-01T00:00:00Z