  A path of a graph $G$ is called a Hamilton path if it passes through all the
vertices of $G$. A graph is Hamilton-connected if any two vertices are
connected by a Hamilton path. Note that any bipartite graph is not
Hamilton-connected. We consider the weak version of Hamilton-connected property
among bipartite graphs. A weakly Hamilton-connected graph is a balanced
bipartite graph $G=(X,Y,E)$ that there is a Hamilton path between any vertex
$x\in X$ and $y\in Y$. In this paper, we present some degrees, number of edges,
and spectral radius conditions for a simple balanced bipartite graph to be
weakly Hamilton-connected.

Combinatorics