Subdivisions of vertex-disjoint cycles in bipartite graphs

Abstract

Let $n\geq 6,k\geq 0$ be two integers. Let $H$ be a graph of order $n$ with $k$ components, each of which is an even cycle of length at least $6$ and $G$ be a bipartite graph with bipartition $(X,Y)$ such that $|X|=|Y|\geq n/2$. In this paper, we show that if the minimum degree of $G$ is at least $n/2-k+1$, then $G$ contains a subdivision of $H$. This generalized an older result of Wang.