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# Ringi Kim (김린기), The strong clique number of graphs with forbidden cycles

## Tuesday, March 31, 2020 @ 4:30 PM - 5:30 PM KST

Room B232, IBS (기초과학연구원)

The strong clique number of a graph $G$ is the maximum size of a set of edges of which every pair has distance at most two.

In this talk, we prove that every  $\{C_5,C_{2k}\}$-free graph has strong clique number at most $k\Delta(G)-(k-1)$, which resolves a conjecture by  Cames van Batenburg et al. We also prove that every $C_{2k}$-free graph has strong clique number at most $(2k−1)\Delta(G) + (2k−1)^2$, improving the previous known upper bound $10k^2 (\Delta(G)-1)$ due to  Cames van Batenburg et al. This is joint work with Eun-Kyung Cho, Ilkyoo Choi, and Boram Park.

## Details

Date:
Tuesday, March 31, 2020
Time:
4:30 PM - 5:30 PM KST
Event Category:
Event Tags:
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Room B232
IBS (기초과학연구원)

## Organizer

Sang-il Oum (엄상일)
Website:
https://dimag.ibs.re.kr/home/sangil/
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209