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X-WR-CALNAME:[gt.go] - 'An analogue to Reed's conjecture for digraphs' par 
 Lucas Picasarri-Arrietta
X-WR-TIMEZONE:Europe/Paris
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TZUNTIL:20261025T010000Z
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DESCRIPTION:Exposé en anglais / Talk in english \n\n\nA simple greedy proce
 dure shows that the chromatic number $\chi(G)$ of a graph $G$ is upper bou
 nded by $\Delta(G)+1$. In 1998\, Reed conjectured that\, in fact\, $\chi(G
 )$ can be bounded halfway between $\Delta(G)+1$ and $\omega(G)$. As a part
 ial result\, he proved the existence of $\epsilon >0$ such that $\chi(G) \
 leq \lceil (1-\epsilon) (\Delta(G)+1) + \epsilon \omega(G) \rceil$\, thus 
 showing that $\chi(G)$ is indeed bounded by a convex combination of $\Delt
 a(G)+1$ and $\omega(G)$. \n\nIn this talk\, we will explore an analogous q
 uestion for digraphs\, where the chromatic number\, the maximum degree\, a
 nd the clique number of a graph are replaced respectively by the dichromat
 ic number\, the maximum geometric mean\, and the biclique number of a digr
 aph. We prove the analogue of Reed’s result\, which also implies an indepe
 ndent result obtained by Harutyunyan and Mohar when restricted to oriented
  graphs. \n\nJoint work with Ken-ichi Kawarabayashi. \nArxiv: https://arxi
 v.org/abs/2407.05827 \n\n[Lucas Picasarri-Arrietta] (NII\, Tokyo) \n\nVéri
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 arks / Remarques \n\nFind all the information of the working group on this
  [ https://graphesetoptimisation.labri.fr/pmwiki.php/Groupe/GT?userlang=en
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 s://graphesetoptimisation.labri.fr/pmwiki.php/Groupe/GT | page web ] . \n
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DTSTART;TZID=Europe/Paris:20241206T140000
DTEND;TZID=Europe/Paris:20241206T150000
LOCATION:LaBRI/178
SEQUENCE:0
SUMMARY:[gt.go] - 'An analogue to Reed's conjecture for digraphs' par Lucas
  Picasarri-Arrietta
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