4 papers
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…
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…
Infinite Schnyder Woods
Louigi Addario-Berry, Emma Hogan, Lukas Michel +1
It is well-known that any finite triangulation possesses a unique maximal Schnyder wood. We introduce Schnyder woods of infinite triangulations, and prove there exists a unique max…
Tight Bounds for Hypercube Minor-Universality
Emma Hogan, Lukas Michel, Alex Scott +3
Benjamini, Kalifa and Tzalik recently proved that there is an absolute constant such that any graph with at most edges and no isolated vertices is a minor of th…