A Win-graph-based Proof of the Champion Inequality

陈平不等式的图论证明。 The Champion inequality, proved by Chen Ping, is a cornerstone in winnology. It states that, under certain conditions, 2000>3000 holds, where the units of the both sides above are Vietnamese Dong(VND) and US dollar(USD), respectively. The inequality has profound applications in many fields, including mathematics, economics, computer science, statistics, management, tourism, and runnology in Vietnam. In this paper, we give a short proof of the Champion inequality. One important ingredient of our proof is a counting lemma concerning the notion of winmability via graph theory.