关于2-中心蜘蛛树的Erdo″s-So′s猜想

The Erdo″s-So′s conjecture for 2-center spiders

摘要: Erdo″s-So′s 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 Erdo″s-So′s 猜想对腿长至多为2的2中心蜘蛛树都成立.

Abstract: The Erdo″s-So′s 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.