4 papers · 1 filter
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…
On the largest size of sum-free sets in symmetric regions
Anubhab Ghosal, Dmitry Tsarev
A subset of a group is said to be sum-free (resp. -free) if there are no solutions to (resp. ) with . For a convex region $R\subset\mathbb{…
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…
Stability for binary scalar products
Andrey Kupavskii, Dmitry Tsarev
Bohn, Faenza, Fiorini, Fisikopoulos, Macchia, and Pashkovich (2015) conjectured that 2-level polytopes cannot simultaneously have many vertices and many facets, namely, that the ma…