Hypercube graph with edge weights
Source: Russian TST 2018, Day 8 P2 (Group NG), P3 (Groups A & B)
March 30, 2023
combinatoricsgraph theory
Problem Statement
There are airports, numbered with binary strings of length . Any two stations whose numbers differ in exactly one digit are connected by a flight that has a price (which is the same in both directions). The sum of the prices of all flights leaving any station does not exceed 1. Prove that one can travel between any two airports by paying no more than 1.