“2021 Combinatorics Workshop” was held from December 20 to December 22, 2021 at Yangpyeong

The 2021 Combinatorics Workshop (2021 조합론 학술대회) was held from December 20, 2021 to December 22, 2021 at the Bloomvista, Yangpyeong. There were 5 invited talks and 12 contributed talks.

Invited Speakers

Speakers of the contributed talks

  • Jungho Ahn, KAIST / IBS DIMAG
  • Jin-Hwan Cho, NIMS
  • Linda Cook, IBS DIMAG
  • Cheolwon Heo, Sungkyunkwan University
  • Seonghyuk Im, KAIST
  • Hyobin Kim, Kyungpook National University
  • Minki Kim, IBS DIMAG
  • Hyemin Kwon, Ajou University
  • Hyunwoo Lee, KAIST
  • Sang June Lee, Kyung Hee University
  • Jaehyeon Seo, KAIST
  • Semin Yoo, KIAS

Organizing Committee

Participants (50 people, all of whom are fully vaccinated against COVID-19)

  • Jungho Ahn, speaker, KAIST / IBS DIMAG
  • Sejeong Bang, session chair, Yeungnam University
  • Rutger Campbell, IBS DIMAG
  • Debsoumya Chakraborti, IBS DIMAG
  • Eun-Kyung Cho, Hankuk University of Foreign Studies
  • Hyunsoo Cho, Ewha Womans University
  • Jin-Hwan Cho, speaker, NIMS
  • Jeong-Ok Choi, organizer/session chair, GIST
  • Linda Cook, speaker, IBS DIMAG
  • Taehyun Eom, KAIST
  • Cheolwon Heo, speaker, Sungkyunkwan University
  • Seonghyuk Im, speaker, KAIST
  • Jihyeug Jang, Sungkyunkwan University
  • Dosang Joe, NIMS
  • Donggyu Kim, KAIST / IBS DIMAG
  • Donghyun Kim, Sungkyunkwan University
  • Dongsu Kim, invited speaker, KAIST
  • Hyobin Kim, speaker, Kyungpook National University
  • Jaehoon Kim, KAIST
  • Jang Soo Kim, Sungkyunkwan University
  • Jinha Kim, IBS DIMAG
  • Minki Kim, speaker, IBS DIMAG
  • Seog-Jin Kim, session chair, Konkuk University
  • Doowon Koh, Chungbuk National University
  • Hyemin Kwon, speaker, Ajou University
  • O-joung Kwon, Incheon National University / IBS DIMAG
  • Dabeen Lee, IBS DIMAG
  • Duksang Lee, KAIST / IBS DIMAG
  • Hyunwoo Lee, speaker, KAIST
  • Joonkyung Lee, invited speaker, Hanyang University
  • Sang June Lee, speaker, Kyung Hee University
  • Seung Jin Lee, Seoul National University
  • Hong Liu, invited speaker, University of Warwick, UK
  • Ben Lund, IBS DIMAG
  • Suil O, invited speaker, SUNY Korea
  • Jaeseong Oh, KIAS
  • Sang-il Oum, organizer/session chair, IBS DIMAG / KAIST
  • Jae Hyun Park, Kyung Hee University
  • Seonjeong Park, invited speaker, Jeonju University
  • Jaehyeon Seo, speaker, KAIST
  • Seunghyun Seo, session chair, Kangwon National University
  • Heesung Shin, organizer/session chair, Inha University
  • Mark Siggers, Kyungpook National University
  • Jaebum Sohn, Yonsei University
  • Minho Song, Sungkyunkwan University
  • U-keun Song, Sungkyunkwan University
  • Jeong Hyun Sung, Seoul National University
  • Tuan Tran, IBS DIMAG
  • Sounggun Wee, KAIST / IBS DIMAG
  • Semin Yoo, speaker, KIAS

Host and Sponsors

Suil O (오수일) gave a talk on the existence of even and odd [a,b]-factors in h-edge-connected r-regular graphs in terms of eigenvalues at the Discrete Math Seminar

On July 6, 2021, Suil O (오수일) from SUNY Korea gave a talk at the Discrete Math Seminar on upper bounds of certain eigenvalues to guarantee the existence of an even or odd [a,b]-factor in h-edge-connected r-regular graphs. The title of his talk was “Eigenvalues and [a, b]-factors in regular graphs“.

Suil O (오수일), Eigenvalues and [a, b]-factors in regular graphs

For positive integers, $r \ge 3, h \ge 1,$ and $k \ge 1$, Bollobás, Saito, and Wormald proved some sufficient conditions for an $h$-edge-connected $r$-regular graph to have a k-factor in 1985. Lu gave an upper bound for the third-largest eigenvalue in a connected $r$-regular graph to have a $k$-factor in 2010. Gu found an upper bound for certain eigenvalues in an $h$-edge-connected $r$-regular graph to have a $k$-factor in 2014. For positive integers $a \le b$, an even (or odd) $[a, b]$-factor of a graph $G$ is a spanning subgraph $H$ such that for each vertex $v \in V (G)$, $d_H(v)$ is even (or odd) and $a \le d_H(v) \le b$. In this talk, we provide best upper bounds (in terms of $a, b$, and $r$) for certain eigenvalues (in terms of $a, b, r$, and $h$) in an $h$-edge-connected $r$-regular graph $G$ to guarantee the existence of an even $[a, b]$-factor or an odd $[a, b]$-factor. This result extends the one of Bollobás, Saito, and Wormald, the one of Lu, and the one of Gu.

Suil O (오수일), An odd [1,b]-factor in regular graphs from eigenvalues

An odd $[1,b]$-factor of a graph is a spanning subgraph $H$ such that for every vertex $v \in V(G)$, $1 \le d_H(v) \le b$, and $d_H(v)$ is odd. For positive integers $r \ge 3$ and $b \le r$, Lu, Wu, and Yang gave an upper bound for the third largest eigenvalue in an $r$-regular graph with even number of vertices to guarantee the existence of an odd [1,b]-factor.
In this talk, we improve their bound.