The depth-first search tree structure of \(TK_{\aleph_ 0}\)-free graphs
The note proves that the following two assertions are equivalent for connected graphs \(G\): (i) \(G\) contains no subdivided infinite complete graph as a subgraph; (ii) \(G\) has a normal spanning tree, that means a depth-first search tree, such that any ray in \(T\) has only finitely many neighbours. This implies a result of Robertson, Seymour and Thomas that these are precisely the graphs of finite tree-width.
scientific article; zbMATH DE number 638664