We prove that if the edges of a graph \(G\) can be colored blue or red in such a way that every vertex belongs to a monochromatic \(k\)-clique of each color, then \(G\) has at least \(4(k-1)\) vertices. This confirms a conjecture of Bucic, Lidicky, Long, and Wagner, and thereby solves the 2-dimensional case of their problem about partitions of discrete boxes with the \(k\)-piercing property. We also characterize the case of equality in our result.
Before the talk, at 3:10pm, there will be tea and cookies in Wean 6220.
The ACO Seminar (2019–2020)