Convidamos todos a prestigiarem a palestra “A Short Path to Kőnig’s, Berge’s, and Hall’s Theorems via Edge-Stability” ministrada pelo docente Daniel Jaume da Universidad Nacional de San Luis.
O evento ocorrerá na sala 102 do prédio 43.112 do Instituto de Matemática e Estatística no dia 10 de junho de 2026 às 15 horas.
Contamos com a presença de todos!
Resumo:
We introduce a simple structural property of bipartite graphs—edge-stability— which states that removing an edge whose endpoints lie in a minimum vertex cover does not change the vertex cover number. This property admits an elementary proof and serves as a bridge between several classical theorems in matching theory. We show that edge-stability follows directly from Kőnig’s Theorem and, conversely, can be used to rederive it. Moreover, we employ edge-stability to obtain short proofs of Berge’s characterization of maximum independent sets and Hall’s Marriage Theorem. Thus within the framework of Reichmeider’s equivalence of Mengerian theorems, edge-stability, Konig’s, Berge’s, and Hall’s theorems are all equivalent. The approach highlights new conceptual and pedagogical connections between these cornerstone results in matching theory.