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Casey Tompkins, Inverse Turán Problems

July 14 Tuesday @ 4:30 PM - 5:30 PM KST

Room B232, IBS (기초과학연구원)

Speaker

For given graphs $G$ and $F$, the Turán number $ex(G,F)$ is defined to be the maximum number of edges in an $F$-free subgraph of $G$. Briggs and Cox introduced a dual version of this problem wherein for a given number $k$, one maximizes the number of edges in a host graph $G$ for which $ex(G,H) < k$.  We resolve a problem of Briggs and Cox in the negative by showing that the inverse Turán number of $C_4$ is $\Theta(k^{3/2})$. More generally, we determine the order of magnitude of the inverse Turán number of $K_{s,t}$ for all $s$ and $t$.  Addressing another problem of Briggs and Cox, we determine the asymptotic value of the inverse Turán number of the paths of length $4$ and $5$ and provide an improved lower bound for all paths of even length.  We also obtain improved bounds on the inverse Turán number of even cycles

Joint work with Ervin Győri, Nika Salia and Oscar Zamora.

Details

Date:
July 14 Tuesday
Time:
4:30 PM - 5:30 PM KST
Event Category:
Event Tags:

Venue

Room B232
IBS (기초과학연구원)

Organizer

Sang-il Oum (엄상일)
Website:
https://dimag.ibs.re.kr/home/sangil/