Hamilton-laceable bi-powers of locally finite bipartite graphs

TL;DR

This paper proves that the third bi-power of a locally finite connected bipartite graph with a perfect matching is Hamilton-laceable, ensuring any two vertices from different classes are connected by a Hamilton arc.

Contribution

It extends Li's result by establishing Hamilton-laceability for the third bi-power of such bipartite graphs.

Findings

Third bi-power of the graph is Hamilton-laceable.

Any two vertices from different bipartition classes are connected by a Hamilton arc.

Strengthens previous results on Hamiltonicity in bipartite graphs.

Abstract

In this paper we strengthen a result due to Li by showing that the third bi-power of a locally finite connected bipartite graph that admits a perfect matching is Hamilton-laceable, i.e. any two vertices from different bipartition classes are endpoints of some common Hamilton arc.