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DTSTART;TZID=America/Toronto:20260306T153000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/tutte-colloq
 uium-kathie-cameron-reconfiguration-vertex
SUMMARY:Tutte Colloquium -Kathie Cameron-Reconfiguration of Vertex Colourin
 gs
CLASS:PUBLIC
DESCRIPTION:SPEAKER:\n Kathie Cameron\n\nAFFILIATION:\n Wilfrid Laurier Uni
 versity\n\nLOCATION:\n MC 5501\n\nABSTRACT: A k-colouring of a graph is a
 n assignment of at most k\ncolours to its vertices so that the ends of eac
 h edge get different\ncolours. We consider two types of “reconfiguration
  steps” for\ntransforming a given k-colouring into a target k-colouring.
  The first\nis to change the colour of a vertex to a colour which does not
  appear\non any of the vertices it is adjacent to. We say that a graph G i
 s\nrecolourable if for every k greater than its chromatic number\, any\nk-
 colouring of G can be transformed into any other by these\nreconfiguration
  steps. The second (more general) type of\nreconfiguration step is Kempe s
 waps. We call a graph Kempe connected\nif for every k\, any k-colouring ca
 n be transformed into any other by\nKempe swaps.\n\nWe have characterized 
 the graphs H such that all graphs which don’t\ncontain H as an induced s
 ubgraph are recolourable\, and done the same\nfor Kempe connectedness. We 
 have shown that modular decomposition and\na stronger version of clique cu
 tsets can be used to show that certain\nclasses are recolourable. We also 
 give some classes of graphs which\nadmit colourings that are “frozen” 
 with respect to these\nreconfiguration steps. \nThis is joint work with Ma
 noj Belavadi and parts are also joint with\nElias Hildred\, Owen Merkel an
 d Dewi Sintiari.
DTSTAMP:20260402T144702Z
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