For a connected graph G, a spanning tree T of G is called a homeomorphically irreducible spanning tree (HIST) if T has no vertices of degree 2. In this talk, we show that if G is a graph of order n≥270 and |N(u)\cup N(v)|≥(n-1)/2 holds for every pair of nonadjacent vertices u and v in G, then G has a HIST, unless G belongs to three exceptional families of graphs or G has a cut-vertex of degree 2. This result improves the latest conclusion, due to Ito and Tsuchiya, that a HIST in G can be guaranteed if d(u) + d(v)≥n-1 holds for every pair of nonadjacent vertices u and v in G.

胡小兰，华中师范大学数学与统计学学院副研究员。2015年于南京大学获理学博士学位，2013年9月至2013年12月在美国西弗吉尼亚大学进行短期学术访问，2017年3月至2018年9月在捷克查理大学交流访问。主持国家自然科学基金面上项目2项，青年项目1项，发表SCI索引论文三十余篇。