Resolving Erdős-Ulam Monochromatic Union-Closed Family Conjectures

Deep Bhattacharjee, Priyabrata Mandal, Ushashi Bhattacharya

We prove both Erdős-Ulam conjectures on monochromatic union-closed families. Every two-colouring of the subsets of a finite set contains a monochromatic union-closed family whose s…