기초과학연구원 이산수학그룹
A vertex colouring of a hypergraph is $c$-strong if every edge $e$ sees at least $\min\{c, |e|\}$ distinct colours. Let $\chi(t,c)$ denote the least number of colours needed so that every $t$-intersecting hypergraph has a $c$-strong colouring. In 2012, Blais, Weinstein and Yoshida introduced this parameter and initiated study on when $\chi(t,c)$ is finite: they …
We will discuss recent progress on the topic of induced subgraphs and tree-decompositions. In particular this talk with focus on the proof of a conjecture of Hajebi that asserts that (if we exclude a few obvious counterexamples) for every integer t, every graph with large enough treewidth contains two anticomplete induced subgraphs each of treewidth …
We provide new constructions of families of quasi-random graphs that behave like Paley graphs but are neither Cayley graphs nor Cayley sum graphs. These graphs give a unified perspective of studying various graphs defined by polynomials over finite fields, such as Paley graphs, Paley sum graphs, and graphs associated with Diophantine tuples and their generalizations …
Since the introduction of cluster algebras by Fomin and Zelevinsky in 2002, there has been significant interest in cluster algebras of surface type. These algebras are particularly noteworthy due to their ability to construct various combinatorial structures like snake graphs, T-paths, and posets, which are useful for proving key structural properties such as positivity or …
Tropical geometry replaces usual addition and multiplication with tropical addition (the min) and tropical multiplication (the sum), which offers a polyhedral interpretation of algebraic variety. This talk aims to pitch the usefulness of tropical geometry in understanding classical algebraic geometry. As an example, we introduce the tropicalization of the variety of symmetric rank 2 matrices. …
For a given hypergraph $H$ and a vertex $v\in V(H)$, consider a random matching $M$ chosen uniformly from the set of all matchings in $H.$ In $1995,$ Kahn conjectured that if $H$ is a $d$-regular linear $k$-uniform hypergraph, the probability that $M$ does not cover $v$ is $(1 + o_d(1))d^{-1/k}$ for all vertices $v\in V(H)$. …
Website: https://cgmt.dimag.kr/ Arrival Date: July 14, 2024 Sunday. Departure Date: July 20, 2024 Saturday. Organizers Ben Lund (IBS Discrete Mathematics Group) Doowon Koh (Chungbuk National University) Sang-il Oum (IBS Discrete Mathematics Group / KAIST)
The 2024 Summer School on Combinatorics and Algorithms is a venue for students and early-career researchers to learn selected topics in theoretical computer science and discrete mathematics. It will be a great opportunity for young and aspiring researchers to study topics which are important but not covered during the lectures in the university classes. This …
Venue Gongju Hanok Vilage (공주한옥마을) Organizers Donggyu Kim (김동규), KAIST and IBS Discrete Mathematics Group Seokbeom Kim (김석범), KAIST and IBS Discrete Mathematics Group Seonghyuk Im (임성혁), KAIST and IBS Extremal Combinatorics and Probability Group Hyunwoo Lee (이현우), KAIST and IBS Extremal Combinatorics and Probability Group
For a family F of graphs, the F-Deletion Problem asks to remove the minimum number of vertices from a given graph G to ensure that G belongs to F. One of the most common ways to obtain an interesting family F is to fix another family H of graphs and let F be the set …