Degree conditions of two vertices with distance two or three for the existence of a Hamilton cycle passing through a matching in a bipartite graph - Chiba, Shuya; Tsugaki, Masao; Yamashita, Tomoki; Yashima, Takamasa (Graphs and combinatorics, 2025)
In 1972, Las Vergnas gave a degree sum conditions for the existence of a perfect matching containing a given matching and for the existence of a Hamilton cycle passing through a given matching. In this paper, we investigate whether we can replace the degree sum conditions in the results due to Las Vergnas with degree conditions of two vertices with distance two or three.