Stability version of Dirac's theorem and its applications for generalized Turán problems
Xiutao Zhu, Ervin Győri, Zhen He, Zequn Lv, Nika Salia, Chuanqi Xiao
Source abstract
Abstract In 1952, Dirac proved that every 2‐connected ‐vertex graph with the minimum degree contains a cycle of length at least . Here we obtain a stability version of this result by characterizing those graphs with minimum degree and circumference at most . We present applications of the above‐stated result by obtaining generalized Turán numbers. In particular, for all we determine how many copies of a five‐cycle as well as four‐cycle are necessary to guarantee that the graph has a circumference larger than . In addition, we give a new proof of Luo's theorem for cliques using our stability result.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.