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SUMMARY:Chromatic number and embeddings
DTSTART:20250625T111500
DTEND:20250625T121500
DTSTAMP:20260416T080622Z
UID:f4ed05b5563682861e779673fad6df610cfdac8499f0921b5003e632
CATEGORIES:Conferences - Seminars
DESCRIPTION:Janos Pach\nWhat makes the chromatic number of a graph large? 
 There have been many attempts to answer this question. The most natural ap
 proach is to look for unavoidable substructures in graphs of large chromat
 ic number. Hadwiger made the conjecture that every graph of chromatic numb
 er r can be transformed into a complete graph of r vertices by a series of
  edge contractions and vertex and edge deletions. This is known to be true
  for r<6. There are several related problems on embeddability properties o
 f graphs that I plan to explain. \n\nThe crossing number of a graph G is 
 the smallest number of edge crossings in a proper drawing of G in the plan
 e. According to Albertson's conjecture\, the crossing number of every grap
 h of chromatic number r is at least as large as the crossing number of a c
 omplete graph with r vertices. We settle Albertson's conjecture for graphs
  whose number of vertices is not much larger than their chromatic number.
  \n\nJoint work with Jacob Fox and Andrew Suk.
LOCATION:MA B1 524 https://plan.epfl.ch/?room==MA%20B1%20524
STATUS:CONFIRMED
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