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DTSTART:20240310T070000
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DTSTART;TZID=America/Toronto:20241119T140000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/graphs-and-m
 atroids-aristotelis-chaniotis-0
SUMMARY:Graphs and Matroids - Aristotelis Chaniotis
CLASS:PUBLIC
DESCRIPTION:TITLE: Induced subgraphs of graphs of large $K_{r}$-free chroma
 tic\nnumber\n\nSPEAKER:\n Aristotelis Chaniotis\n\nAFFILIATION:\n Universi
 ty of Waterloo\n\nLOCATION:\n MC 5417\n\nABSTRACT:For an integer $r\\geq 2
 $\, the $K_{r}$-free chromatic number\nof a graph $G$\, denoted by $\\chi_
 {r}(G)$\, is the minimum size of a\npartition of the set of vertices of $G
 $ into parts each of which\ninduces a $K_{r}$-free graph. In this setting\
 , the $K_{2}$-free\nchromatic number is the usual chromatic number. Which 
 are the\nunavoidable induced subgraphs of graphs of large $K_{r}$-free\nch
 romatic number? Generalizing the notion of $\\chi$-boundedness\, we\nsay t
 hat a hereditary class of graphs is $\\chi_{r}$-bounded if there\nexists a
  function which provides an upper bound for the $K_{r}$-free\nchromatic nu
 mber of each graph of the class in terms of the graph's\nclique number. Wi
 th an emphasis on a generalization of the\nGy\\'arf\\'as-Sumner conjecture
  for $\\chi_{r}$-bounded classes of graphs\nand on polynomial $\\chi$-boun
 dedness\, I will discuss some recent\ndevelopments on $\\chi_{r}$-boundedn
 ess and related open problems.\nBased on joint work with Mathieu Rundstr\\
 \"om and Sophie Spirkl.
DTSTAMP:20260402T144515Z
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