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Progress on Albertson's Conjecture
Daniel W. Cranston
Albertson conjectured that every graph with chromatic number has crossing number at least the crossing number of the complete graph . This conjecture was proved for $r\le…
Equitably Coloring Planar and Outerplanar Graphs
Daniel W. Cranston, Reem Mahmoud
A proper -coloring of an -vertex graph is \emph{equitable} if every color class has size or . A necessary condition to have an equita…
A Linear Kernel for Independent Set Reconfiguration in Planar Graphs
Nicolas Bousquet, Daniel W. Cranston
Fix a positive integer , and a graph that is -minor-free. Let and be two independent sets in , each of size . We begin with a ``token'' on each ve…
Reconfiguration of List Colourings
Stijn Cambie, Wouter Cames van Batenburg, Daniel W. Cranston +2
Given a proper (list) colouring of a graph , a recolouring step changes the colour at a single vertex to another colour (in its list) that is currently unused on its neighbours,…