Vertex-disjoint hexagons with chords in a bipartite graph Original Research Article

In this paper, we explore vertex-disjoint subgraphs in a bipartite graph. Let G = (V1, V2; E) be a bipartite graph with |V1| = |V2| = sk, where s ⩾ 2 and k ⩾ 1 are integers. We conjecture that if the minimum degree of G is at least (s − 1)k + 1, then G contains k vertex-disjoint subgraphs isomorphic to Ks,s. We verify this conjecture for k ⩽ 3. When s = 3, we show that G contains k vertex-disjoint hexagons such that each of them has two chords, i.e., Gࣴk(K3,3 − e).