Progress on sufficient conditions for a graph to have a spanning $k-$ended tree

Pham Hoang Ha

In 1998, Broersma and Tuinstra [J. Graph Theory \textbf{29} (1998), 227-237] proved that if $G$ is a connected graph satisfying ${\sigma }_2(G)\ge |G|-k+1$ then $G$ has a spanning $k-$en…