Route systems and bipartite graphs
Ladislav Nebeský · Czechoslovak Mathematical Journal · 1991
Route systems, which are defined in the present paper, generalize the systems of all shortest paths of connected graphs.The route systems which are the systems of all shortest paths of connected bipartite graphs will be characterized here.We first make some conventions concerning sequences.Let Fbe a finite nonempty set.We denote by £f N (V) the set of all sequences (u 1? ..., Uj) such that j ^ 1 and u l5 ..., Uj є V. Let k ^ 1, and let v l9 ..., v k є V; if we denote a = (v u ..., v k ), then we shall write |a| = k and ä = (v h ,..., v^.Let m ^ 2, let n 1? ..., n m ^ 1, and let Wii, • •-, w 1;ll ,..., w ml , ..., w mnm e V; if we denote ßi =(wii,...,w lfI1 ),