# Subdivisions of vertex-disjoint cycles in bipartite graphs

## TL;DR

This paper proves that bipartite graphs with sufficiently high minimum degree contain subdivisions of certain disjoint even cycles, extending previous results in graph theory.

## Contribution

It generalizes Wang's earlier theorem by establishing conditions for subdivisions of multiple even cycles in bipartite graphs.

## Key findings

- Bipartite graphs with minimum degree at least n/2 - k + 1 contain subdivisions of specified disjoint even cycles.
- The result applies to graphs with multiple components, each being an even cycle of length at least 6.
- The theorem extends classical cycle subdivision results to more complex bipartite structures.

## 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.