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X-WR-CALNAME:[gt.go] - 'Disjoint odd circuits in a bridgeless cubic graph c
 an be quelled by a single perfect matching' by František Kardoš
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TZUNTIL:20240331T010000Z
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DTSTART:20211031T030000
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RDATE:20221030T030000
RDATE:20231029T030000
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DESCRIPTION:/Exposé en anglais/Talk in english/ \n\nLet G be a bridgeless c
 ubic graph. The Berge-Fulkerson Conjecture (1970s) states that G admits a 
 list of six perfect matchings such that each edge of G belongs to exactly 
 two of these perfect matchings. If answered in the affirmative\, two other
  recent conjectures would also be true: the Fan-Raspaud Conjecture (1994)\
 , which states that G admits three perfect matchings such that every edge 
 of G belongs to at most two of them\; and a conjecture by Mazzuoccolo (201
 3)\, which states that G admits two perfect matchings whose deletion yield
 s a bipartite subgraph of G. It can be shown that given an arbitrary perfe
 ct matching of G\, it is not always possible to extend it to a list of thr
 ee or six perfect matchings satisfying the statements of the Fan-Raspaud a
 nd the Berge-Fulkerson conjectures\, respectively. In this talk\, we show 
 that given any 1+-factor F (a spanning subgraph of G such that its vertice
 s have degree at least 1) and an arbitrary edge e of G\, there always exis
 ts a perfect matching M of G containing e such that G∖(F∪M) is bipartite. 
 Our result implies Mazzuoccolo's conjecture\, but not only. It also implie
 s that given any collection of disjoint odd circuits in G\, there exists a
  perfect matching of G containing at least one edge of each circuit in thi
 s collection. \n\nThis is a joint work with Edita Máčajová and Jean Paul Z
 erafa. \n\n\n[František Kardoš] (Université de Bordeaux\, LaBRI ) \n\nhttp
 s://www.labri.fr/perso/fkardos/ \n\n\nRemarks / Remarques \n\nFind all the
  information of the working group on this [ https://graphesetoptimisation.
 labri.fr/pmwiki.php/Groupe/GT?userlang=en | web page ] . \nRetrouvez toute
 s les informations du GT sur cette [ https://graphesetoptimisation.labri.f
 r/pmwiki.php/Groupe/GT | page web ] .
DTSTART;TZID=Europe/Paris:20220617T140000
DTEND;TZID=Europe/Paris:20220617T150000
LOCATION:https://webconf.u-bordeaux.fr/b/mar-ef4-zed ou au LaBRI/178
SEQUENCE:0
SUMMARY:[gt.go] - 'Disjoint odd circuits in a bridgeless cubic graph can be
  quelled by a single perfect matching' by František Kardoš
TRANSP:OPAQUE
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