We are given a finite, simple, non-directed graph. Ann writes positive real numbers on each edge of the graph such that for all vertices the following is true: the sum of the numbers written on the edges incident to a given vertex is less than one. Bob wants to write non-negative real numbers on the vertices in the following way: if the number written at vertex v is v0, and Ann's numbers on the edges incident to v are e1,e2,…,ek, and the numbers on the other endpoints of these edges are v1,v2,…,vk, then v0=∑i=1keivi+2022. Prove that Bob can always number the vertices in this way regardless of the graph and the numbers chosen by Ann.Proposed by Boldizsár Varga, Verőce graph theorycombinatoricslinear algebraprobabilitykomal