SEMINARS
Spanning $k$-ended trees in quasi-claw-free graphs

2017-07-05　10:30 — 14:00

Middle Lecture Room

Let $N[v]=N(v)\cup\{v\}$ and $J(u,v)=\{w\in N(u)\cap N(v):N(w)\subseteq N[u]\cup N[v]\}$. A graph $G$ is called quasi-claw-free if $J(u,v)\neq \emptyset$ for any $u,v\in V(G)$ with $d(u,v)=2$. Here, we show that if $G$ is a connected quasi-claw-free graph with $\sigma_{k+1}(G)\geq |G|-k,$ then $G$ contains a spanning $k$-ended tree, which generalizes some known results. This result holds for some graphs containing $K_{1,4}$ subgraphs, which are not contained in the graphs discussed by Kyaw (Discrete Math. 31(2011) 2135-2142).