Geodesic
Balancing connected colourings of graphs
The electronic journal of combinatorics, Tome 30 (2023) no. 1
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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.
DOI : 10.37236/11256
Classification : 05C15
Mots-clés : factorization, spanning tree, tree packing, balance, Henneberg sequence

Freddie Illingworth  1   ; Emil Powierski  1   ; Alex Scott  1   ; Youri Tamitegama  1

1 University of Oxford 
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Freddie Illingworth; Emil Powierski; Alex Scott; Youri Tamitegama. Balancing connected colourings of graphs. The electronic journal of combinatorics, Tome 30 (2023) no. 1. doi: 10.37236/11256

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