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math.CO2026
Colour-balanced subgraphs
Emma Hogan, Alex Scott, Dmitry Tsarev
A -edge-coloured graph is colour-balanced if each colour appears equally often. Resolving a conjecture of Pardey and Rautenbach, we show that any colour-balanced -edge-colour…
math.CO2026
Anticoncentration of random spanning trees in graphs with large minimum degree
Veronica Bitonti, Lukas Michel, Alex Scott
A classical result by Otter shows that the complete graph has an exponential number of non-isomorphic spanning trees. This was recently extended by Lee to every almost regular grap…