Decomposition of wheel-and-parachute-free balanced bipartite graphs
The main notions of the paper are the notions of wheel and parachute. A cycle in a graph is called a hole if no two nonconsecutive nodes of it are adjacent. A wheel \((H, x)\) is defined to be the subgraph induced by a hole \(H\) and a node \(x\) not belonging to \(H\) but having at least three neighbours in \(H\). The definition of parachute is too lengthy to reproduce it here. In a drawing the parachute resembles a plane version of a usual one. A bipartite graph is called balanced if it does not contain a hole of length \(4k+ 2\). The paper is devoted to balanced bipartite graphs that contain neither a wheel nor a parachute as an induced subgraph.
scientific article; zbMATH DE number 806410
scientific article