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X-WR-CALNAME:[gt.go] - 'On modular colourings of graphs' by Pedro Mariano V
 iana Neto
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TZUNTIL:20271031T010000Z
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DESCRIPTION:Given a graph $G$ and an integer $k \geq 2$\, let $\chi'_k(G)$ 
 denote the minimum number of colours required to colour the edges of $G$ s
 uch that\, in each colour class\, the subgraph induced by the edges of tha
 t colour has all non-zero degrees congruent to $1$ modulo $k$. In 1992\, P
 yber proved that $\chi'_2(G) \leq 4$ for every graph $G$\, and posed the q
 uestion of whether $\chi'_k(G)$ can be bounded solely in terms of $k$ for 
 every $k \geq 3$. This question was answered in 1997 by Scott\, who showed
  that $\chi'_k(G) \leq 5k^2 \log k$\, and further asked whether $\chi'_k(G
 ) = O(k)$. Recently\, Botler\, Colucci\, and Kohayakawa (2023) answered Sc
 ott’s question affirmatively\, proving that $\chi'_k(G) \leq 198k - 101$\,
  and conjectured that the multiplicative constant could be reduced to $1$.
  A step towards this latter conjecture was made in 2024 by Nweit and Yang\
 , who improved the bound to $\chi'_k(G) \leq 177k - 93$. \n\nIn this talk\
 , we will discuss the details of how we reduced this multiplicative consta
 nt to $9$ and present further open questions concerning modular colouring 
 of graphs. \n\n\n\n(Pedro Mariano Viana Neto) [Instituto de Matemática e E
 statística\, São Paulo] \n\n\nVérifiez que vous êtes bien inscrits sur le 
 site du [gdr-ifm-gt-graphes] : [ https://gtgraphes.labri.fr/pmwiki/pmwiki.
 php/Equipes/Equipes#membres | https://gtgraphes.labri.fr/pmwiki/pmwiki.php
 /Equipes/Equipes#membres ] \n\nRemarks / Remarques \n\nFind all the inform
 ation of the working group on this [ https://graphesetoptimisation.labri.f
 r/pmwiki.php/Groupe/GT?userlang=en | web page ] . \nRetrouvez toutes les i
 nformations du GT sur cette [ https://graphesetoptimisation.labri.fr/pmwik
 i.php/Groupe/GT | page web ] . \n\n\n\nImport automatique depuis https://w
 ebmel.u-bordeaux.fr/home/bf-labri.ca@u-bordeaux.fr/gt.go.ics par sync_ical
 s_to_drupal.py pour GT-GO
DTSTART;TZID=Europe/Paris:20260306T140000
DTEND;TZID=Europe/Paris:20260306T150000
LOCATION:LaBRI/178
SEQUENCE:0
SUMMARY:[gt.go] - 'On modular colourings of graphs' by Pedro Mariano Viana 
 Neto
TRANSP:OPAQUE
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