A characterization of planar graphs by Trémaux orders (Q1065816)

A Trémaux tree (or Depth-First-Search tree) of a graph G is a rooted spanning tree (T,r) in G (considered also as a semi-lattice with lowest element r) such that every edge outside T is incident with two comparable vertices in T. A characterization theorem of planar graphs based on the concept of Trémaux tree is stated and proved. The theorem can be used as a topological tool to justify planarity testing algorithms involving Depth-First-Search.