Power of pl am dle iven an infinite planar graph. If its every finite subgraph is k-colorable, then the graph itself is also k-colorable Example Every set S can be(totally) ordered Theorem An infinite tree with finite branches has an infinite pathPower of PL . Example . . Given an infinite planar graph. If its every finite subgraph is k-colorable, then the graph itself is also k-colorable. . Example . .Every set S can be (totally) ordered. . Theorem . .An infinite tree with finite branches has an infinite path. Yi Li (Fudan University) Discrete Mathematics May 7, 2013 4 / 20