MathDB

Each edge of a complete graph with

101

vertices is marked with

1

-1

. It is known that absolute value of the sum of numbers on all the edges is less than

150

. Prove that the graph contains a path visiting each vertex exactly once such that the sum of numbers on all edges of this path is zero.
(Y. Caro, A. Hansberg, J. Lauri, C. Zarb)

Problem Statement