A counterexample to the Alon-Saks-Seymour conjecture and related problems
Abstract
Consider a graph obtained by taking edge disjoint union of k complete bipartite graphs. Alon, Saks and Seymour conjectured that such graph has chromatic number at most k+1. This well known conjecture remained open for almost twenty years. In this paper, we construct a counterexample to this conjecture and discuss several related problems in combinatorial geometry and communication complexity.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.