BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//labri.fr//NONSGML kigkonsult.se iCalcreator 2.41.92//
CALSCALE:GREGORIAN
METHOD:PUBLISH
UID:d587d4f3-829c-4550-8124-6a724f43e7df
X-WR-CALNAME:[gt.go] - 'Criticality in Sperner's Lemma' by Tomas Kaiser
X-WR-TIMEZONE:Europe/Paris
BEGIN:VTIMEZONE
TZID:Europe/Paris
TZUNTIL:20260329T010000Z
BEGIN:STANDARD
TZNAME:CET
DTSTART:20231029T030000
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
RDATE:20241027T030000
RDATE:20251026T030000
END:STANDARD
BEGIN:DAYLIGHT
TZNAME:CEST
DTSTART:20240331T020000
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
RDATE:20250330T020000
END:DAYLIGHT
END:VTIMEZONE
BEGIN:VEVENT
UID:d587d4f3-829c-4550-8124-6a724f43e7df
DTSTAMP:20260420T051629Z
CLASS:PUBLIC
DESCRIPTION:/Exposé /Talk/ \n\nSperner's lemma states that if a labelling o
 f the vertices of a triangulation $K$ of the $d$-simplex $\Delta^d$ with l
 abels $1\, 2\, ...\, d+1$ has the property that (i) each vertex of $\Delta
 ^d$ receives a distinct label\, and (ii) any vertex lying in a face of $\D
 elta^d$ has the same label as one of the vertices of that face\, then ther
 e exists a rainbow facet (a facet whose vertices have pairwise distinct la
 bels). \n\nTibor Gallai observed that Sperner's Lemma was equivalent to th
 e claim that certain graphs associated to the triangulations of $\Delta^d$
  are $(d+2)$-chromatic\, and he asked in 1969 whether these graphs are in 
 fact $(d+2)$-critical. (The question is included as Problem 9.14 in Jensen
  and Toft's collection \emph{Graph Coloring Problems}.) \n\nIn this talk\,
  we show that the answer is affirmative for $d\leq 2$ (as already proved b
 y Gallai)\; for every $d\geq 3$\, however\, we answer Gallai's question in
  the negative by constructing an infinite family of examples where no labe
 lling with the requested property exists. The construction is based on the
  properties of a convex $4$-polytope which had been used earlier to dispro
 ve a claim of Theodore Motzkin on neighbourly polytopes. \n\nJoint work wi
 th Matěj Stehlík and Riste Škrekovski \n\n[Tomas Kaiser ] (Faculty of Appl
 ied Sciences\, Pilsen ) \nhttps://home.zcu.cz/~kaisert/ \n\nRemarks / Rema
 rques \n\nFind all the information of the working group on this [ https://
 graphesetoptimisation.labri.fr/pmwiki.php/Groupe/GT?userlang=en | web page
  ] . \nRetrouvez toutes les informations du GT sur cette [ https://graphes
 etoptimisation.labri.fr/pmwiki.php/Groupe/GT | page web ] .
DTSTART;TZID=Europe/Paris:20240614T140000
DTEND;TZID=Europe/Paris:20240614T150000
LOCATION:LaBRI/178
SEQUENCE:0
SUMMARY:[gt.go] - 'Criticality in Sperner's Lemma' by Tomas Kaiser
TRANSP:OPAQUE
END:VEVENT
END:VCALENDAR
