Turán Problems for Suspension of a Balanced Tree
Xiutao Zhu, Xiaolin Wang, Yanbo Zhang, Fangfang Zhang · Journal of Graph Theory · 2026
ABSTRACT The Turán number is the maximum number of edges that an ‐vertex ‐free graph can have. The suspension is obtained from by adding a new vertex which is adjacent to all vertices of and a tree is balanced if the size of one color class is and the other is or . In this paper, we obtain a sharp bound of when based on the Erdős‐Sós Conjecture. We also show the bound is sharp for infinitely many and characterize all extremal graphs. In particular, if satisfies some conditions such as contains a matching covering all vertices in one color class, then the bound is sharp for all . This is a new class of graphs whose decomposition family does not contain a linear forest but we still can determine its Turán number.