Simpler Proof and a Generalization of the Zero-Trees Theorem

摘要

Z. Furedi and D. J. Kleitman proved that if an integer weight is assigned to eachedge of a complete graph on p + 1 vertices, then some spanning tree has total weight divisible by p. A simpler proof is obtained by generalizing the result to hypergraphs. The various steps of the proof are presented and each step of the proof is justified.