Each edge of a complete graph with 101 vertices is marked with 1 or ā1. 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) combinatoricsgraph theory