{"id":2240,"date":"2026-06-09T07:53:45","date_gmt":"2026-06-09T10:53:45","guid":{"rendered":"https:\/\/www.ufrgs.br\/ppgmap\/?p=2240"},"modified":"2026-06-09T07:53:45","modified_gmt":"2026-06-09T10:53:45","slug":"palestra-a-short-path-to-konigs-berges-and-halls-theorems-via-edge-stability","status":"publish","type":"post","link":"https:\/\/www.ufrgs.br\/ppgmap\/?p=2240","title":{"rendered":"Palestra &#8211; A Short Path to K\u0151nig\u2019s, Berge\u2019s, and Hall\u2019s Theorems via Edge-Stability"},"content":{"rendered":"<p style=\"text-align: justify;\"><span style=\"font-family: arial, helvetica, sans-serif;\">Convidamos todos a prestigiarem a palestra &#8220;<strong><em>A Short Path to K\u0151nig\u2019s, Berge\u2019s, and Hall\u2019s Theorems via Edge-Stability<\/em><\/strong>&#8221; ministrada pelo docente\u00a0Daniel Jaume da\u00a0Universidad Nacional de San Luis.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: arial, helvetica, sans-serif;\">O evento ocorrer\u00e1 na sala 102 do pr\u00e9dio 43.112 do Instituto de Matem\u00e1tica e Estat\u00edstica no dia 10 de junho de 2026 \u00e0s 15 horas.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: arial, helvetica, sans-serif;\">Contamos com a presen\u00e7a de todos!<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: arial, helvetica, sans-serif;\">Resumo:<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: arial, helvetica, sans-serif;\">We introduce a simple structural property of bipartite graphs\u2014edge-stability\u2014\u00a0which 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 K\u0151nig\u2019s Theorem and, conversely, can be used to rederive it. Moreover,\u00a0 we employ edge-stability to obtain short proofs of Berge&#8217;s characterization of maximum independent sets and Hall&#8217;s Marriage Theorem. Thus within the framework of Reichmeider&#8217;s equivalence of Mengerian theorems, edge-stability, Konig&#8217;s, Berge&#8217;s, and Hall&#8217;s theorems are all equivalent. The approach highlights new conceptual and pedagogical connections between these cornerstone results in matching theory.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Convidamos todos a prestigiarem a palestra &#8220;A Short Path to K\u0151nig\u2019s, Berge\u2019s, and Hall\u2019s Theorems via Edge-Stability&#8221; ministrada pelo docente\u00a0Daniel Jaume da\u00a0Universidad Nacional de San &hellip; <\/p>\n","protected":false},"author":1,"featured_media":2241,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-2240","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sem-categoria"],"_links":{"self":[{"href":"https:\/\/www.ufrgs.br\/ppgmap\/index.php?rest_route=\/wp\/v2\/posts\/2240","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ufrgs.br\/ppgmap\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ufrgs.br\/ppgmap\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ufrgs.br\/ppgmap\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ufrgs.br\/ppgmap\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2240"}],"version-history":[{"count":1,"href":"https:\/\/www.ufrgs.br\/ppgmap\/index.php?rest_route=\/wp\/v2\/posts\/2240\/revisions"}],"predecessor-version":[{"id":2242,"href":"https:\/\/www.ufrgs.br\/ppgmap\/index.php?rest_route=\/wp\/v2\/posts\/2240\/revisions\/2242"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.ufrgs.br\/ppgmap\/index.php?rest_route=\/wp\/v2\/media\/2241"}],"wp:attachment":[{"href":"https:\/\/www.ufrgs.br\/ppgmap\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2240"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ufrgs.br\/ppgmap\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2240"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ufrgs.br\/ppgmap\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}