Speaker
Nika Salia
(IBS Extremal Combinatorics and Probability Group)
Description
In 1952, Dirac proved that every $2$-connected $n$-vertex graph with the minimum degree $k+1$ contains a cycle of length at least $\min\{n, 2(k+1)\}$. Here we obtain a stability version of this result by characterizing those graphs with minimum degree $k$ and circumference at most $2k+1$.
We present applications of the above-stated result by obtaining generalized Tur\'an numbers.
In particular, for all $\ell \geq 5$ 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 $\ell$.
In addition, we give new proof of Luo's Theorem for cliques using our stability result.
Primary authors
Mr
Zhu Xiutao
( Nanjing University)
Ervin Győri
Zhen He
Mr
Lv Zequn
Nika Salia
(IBS Extremal Combinatorics and Probability Group)
Ms
Xiao Chuanqi
