Decomposition of wheel-and-parachute-free balanced bipartite graphs Original Research Article

A wheel in a bipartite graph is an induced subgraph defined by a chordless cycle H together with a node v having at least three neighbors in H. A parachute in a bipartite graph is an induced subgraph defined by four chordless paths T,P1,P2,M of positive lengths, T = v1, …, v2; P1 = v1,…, z; P2 = v2, …, z; M = v,…, z, where (v1,v2,v,z) are distinct nodes, and two edges vv1 and vv2. The parachute contains no other edge except the ones mentioned above. Furthermore ¦E(P1)¦ + ¦E(P2)¦ ⩾ 3. A cycle C in a bipartite graph is said to be quad if its length is congruent to 0 mod 4. C is unquad if its length is congruent to 2 mod 4.