Seminário de Teoria Espectral de Grafos e Aplicações – Daniel Jaume (Universidad Nacional de San Luis, Argentina) – 26/05/25 – 14h
Na próxima segunda-feira, dia 26/05, teremos mais uma edição dos nossos Seminários de Teoria Espectral de Grafos e Aplicações.
Seguem abaixo as informações
Palestrante: Daniel Jaume, Universidad Nacional de San Luis, Argentina.
Title: Determinantal properties of graphs with large independent number
Abstract: We investigate structural and determinantal properties of graphs whose independence number is at least half their order. We refer to such graphs as \emph{meager graphs}. This class encompasses a wide range of sparse graphs, including matchable K\H{o}nig-Egerv\'{a}ry graphs, and exhibits rich combinatorial and algebraic behavior.
Our main result shows that every meager graph admits a bipartite spanning subgraph with the same determinant and permanent as the original graph. This unveils a remarkable symmetry in the Sachs subgraph expansion and highlights deep connections between algebraic and combinatorial graph invariants.
We further introduce a new reduction technique based on the deletion of certain subgraphs, which we call \emph{c-ears}. We prove that the determinant is invariant up to sign under the removal of c-ears, providing a tool for structural simplification without altering key algebraic characteristics.
These findings open the path toward a characterization of vertex-minimal meager graphs and suggest new avenues for the study of determinantal invariants in the context of sparse graph theory.
co-authors:
Daniel A Jaume, Diego G. Martinez, Gonzalo Molina, Cristian Panelo, and Kevin Pereyra.
Como sempre, nos encontraremos pelo Google Meet:
Seminário de Teoria Espectral de Grafos e Aplicações
Segunda-feira, 26 de maio · 2:00 – 3:00pm
Fuso horário: America/Sao_Paulo
Como participar do Google Meet
Link da videochamada: https://meet.google.com/keq-qghc-zks
Esperamos vocês!