Graphs inducing totally balanced and submodular Chinese postman games

A Chinese postman (CP) game is induced by a weighted undirected, connected graph in which the edges are identified as players and a vertex is chosen as post-office location.Granot and Granot (2012) characterized graphs that give rise to CP games that are balanced. This note completes this line of research by characterizing graphs that give rise to CP games that are submodular (totally balanced, respectively).