기초과학연구원 이산수학그룹
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This talk is an introduction to the recent notion of merge-width, proposed by Jan Dreier and Szymon Torúnczyk. I will give an overview of the context and motivations for merge-width, namely the first-order model checking problem, and present the definition, some examples, and some basic proof techniques with the example of χ-boundedness. This is based … |
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We formulate a geometric version of the Erdős-Hajnal conjecture that applies to finite projective geometries rather than graphs. In fact, we give a natural extension of the 'multicoloured' version of the Erdős-Hajnal conjecture. Roughly, our conjecture states that every colouring of the points of a finite projective geometry of dimension $n$ not containing a fixed … |
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The matroid intersection problem is a fundamental problem in combinatorial optimization. In this problem we are given two matroids and the goal is to find the largest common independent set in both matroids. This problem was introduced and solved by Edmonds in the 70s. The importance of matroid intersection stems from the large variety of … |
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Website: https://cw2025.combinatorics.kr Invited Speakers Dongsu Kim (KAIST) Eun Jung Kim (KAIST) O-joung Kwon (Hanyang University) Ae Ja Lee (Pennsylvania State University) Zhicong Lin (Shandong University) Organizing Committee Sang-il Oum (엄상일), IBS Discrete Mathematics Group Jang Soo Kim (김장수), Sungkyunkwan University Seunghyun Seo (서승현), Kangwon National University |
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Venue The K-Hotel Gyeongju Website https://indico.ibs.re.kr/e/kscw2025 Organizers Seokbeom Kim (김석범), KAIST and IBS Discrete Mathematics Group Hyunwoo Lee (이현우), KAIST and IBS Extremal Combinatorics and Probability Group Jaehyeon Seo (서재현), Yonsei University Kyungjin Cho (조경진), POSTECH |
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We prove that for any circle graph $H$ with at least one edge and for any positive integer $k$, there exists an integer $t=t(k,H)$ so that every graph $G$ either has a vertex-minor isomorphic to the disjoint union of $k$ copies of $H$, or has a $t$-perturbation with no vertex-minor isomorphic to $H$. Using the … |
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Lehel's conjecture states that every 2-edge-colouring of the complete graph $K_n$ admits a partition of its vertices into two monochromatic cycles. This was proven for sufficiently large n by Luczak, Rödl, and Szemerédi (1998), extended by Allen (2008), and fully resolved by Bessy and Thomassé in 2010. We consider a rainbow version of Lehel's conjecture … |
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