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arXiv · 1809.05265

The degrees, number of edges, spectral radius and weakly Hamilton-connectedness of bipartite graphs

Jia Wei·Zhifu You
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Abstract

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.

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Jia Wei, Zhifu You. 2018-09-14. The degrees, number of edges, spectral radius and weakly Hamilton-connectedness of bipartite graphs. https://arxiv.org/abs/1809.05265

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