关于2-中心蜘蛛树的Erdös-Sós猜想

The Erdös-Sós conjecture for 2-center spiders

Erdös-Sós猜想:如果图G平均度大于k-2,则G包含任一k个顶点的数.蜘蛛树是指最多只有一个点度超过2的树.范更华、洪艳梅和刘清海证明了该猜想对所有蜘蛛树成立.本文我们定义2中心蜘蛛树为至多两个相邻点度超过2的树并且证明了Erdös-Sós猜想对腿长至多为2的2中心蜘蛛树都成立.

The Erdös-Sós Conjecture states that if G is a graph with average degree more than k-2,then G contains every tree on k vertices.A spider can be seen as a tree with at most one vertex of degree more than two.Fan,Hong,and Liu proved that the conjecture holds for spiders.In this note,we define a 2-center spider as a tree with at most two adjacent vertices of degree more than two and show that the Erdös-Sós Conjecture holds for 2-center spiders with legs of lengths at most two adjacent vertices of degree more than 2 as 2-center spider.We prove that if G is a graph on n vertices with average degree more than k-2,then G contains every 2-center spider with k vertices,where length of 2-center spider′legs is no more than 2.