Connected k-factors in bipartite graphs

Let k,l be two positive integers. An S-k,S-l is a graph obtained from disjoint K-1,K-k and K-1,K-l by adding an edge between the k-degree vertex in K-1,K-k and the l-degree vertex in K-1,K-l. An S-k,S-l-free graph is a graph containing no induced subgraph isomorphic to S-k,S-l. In this paper, we show that, for any two positive integers k,l with 2 <= k <= l, there exists a constant c=c(k,l) such that every connected balanced S-k,S-l-free bipartite graph with minimum degree at least c contains a connected k-factor. (C) 2022 Elsevier B.V. All rights reserved.