Balancing Connected Colourings of Graphs

  • Freddie Illingworth
  • Emil Powierski
  • Alex Scott
  • Youri Tamitegama


We show that the edges of any graph $G$ containing two edge-disjoint spanning trees can be blue/red coloured so that the blue and red graphs are connected and the blue and red degrees at each vertex differ by at most four. This improves a result of Hörsch. We discuss variations of the question for digraphs, infinite graphs and a computational question, and resolve two further questions of Hörsch in the negative.

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