Maximizing several cuts simultaneously
Abstract
Consider two graphs G1 and G2 on the same vertex set V and suppose that Gi has mi edges. Then there is a bipartition of V into two classes A and B so that for both i=1,2 the number of edges between A and B in Gi is (1+o(1))mi/2. This answers a question of Bollobas and Scott. We also prove results about partitions into more than two vertex classes.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.