arXiv subjects
Publications and source records attributed to Nguyen Hoang Trang.
In this paper, we prove that every $n$-vertex connected $K_{1,5}$-free graph $G$ with $σ_4(G)\geq n-1$ contains a spanning tree with at most $5$ leaves and branch vertices in total. Moreover, the degree sum condition "$σ_4(G)\geq n-1$" is best possible.
In this article, we study the modified defect relations of the Gauss map of complete minimal surfaces in $\mathbb R^3$ and $ \mathbb R^4$ on annular ends. We obtain results which are similar to the ones obtained by Fujimoto~[J. Differential Geometry \textbf{29} (1989), 245-262] for (the whole) complete minimal surfaces. We thus give some improvements of the previous results for the Gauss maps of complete minimal surfaces restricted on annular ends.