On August 24, Monday, the 2020 Combinatorics Workshop (2020 조합론 학술대회) was held online due to the COVID-19 pandemic. This local workshop series began in 2004 and has been continued to be one of the biggest annual gathering of people in combinatorics located in Korea. Due to the COVID-19 pandemic, it has been reduced to a one-day online conference on Zoom. It was hosted by Kyung Hee University and IBS Discrete Mathematics Group.
Combinatorics Workshop (조합론 학술대회) is the biggest annual conference in combinatorics in Korea. It was firstly held in 2004 by the Yonsei University BK21 Research Group. It has been advised by the committee of discrete mathematics of the Korean Mathematical Society since 2013. The aim of this workshop is to bring active researchers with different backgrounds to discuss recent and prospective advances in combinatorics and related areas.
Originally, we planned an offline workshop. However, COVID 19 is more spreading and many participants are worried about attending an offline conference. So the schedule and venue are changed as an online workshop with Zoom. I hope that all participants generously understand this sudden change.
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.
