Jaehoon Kim (김재훈), A resilience version of Pósa’s theorem

Room B232 IBS (기초과학연구원)

Pósa's theorem states that any graph G whose degree sequence $d_1\leq \dots \leq d_n$ satisfies $d_i \geq i+1$ for all $i< n/2$ has a Hamilton cycle. This degree condition is best possible. We show that a similar result holds for suitable subgraphs $G$ of random graphs. This is joint work with Padraig Condon, Alberto Espuny

Dennis Wong, Generating Gray codes and universal cycles for weak orders

Room B232 IBS (기초과학연구원)

A weak order is a way to rank n objects where ties are allowed. Weak orders have applications in diverse areas such as linguistics, designing combination locks, and even in horse racing. In this talk, we present new and simple algorithms to generate Gray codes and universal cycles for weak orders.

Seog-Jin Kim (김석진), Online DP-coloring of graphs

Room B232 IBS (기초과학연구원)

Online list coloring and DP-coloring are generalizations of list coloring that attracted considerable attention recently. Each of the paint number, $\chi_P(G)$, (the minimum number of colors needed for an online coloring of $G$) and the DP-chromatic number, $\chi_{DP}(G)$, (the minimum number of colors needed for a DP-coloring of $G$) is at least the list chromatic

Casey Tompkins, Inverse Turán Problems

Room B232 IBS (기초과학연구원)

For given graphs $G$ and $F$, the Turán number $ex(G,F)$ is defined to be the maximum number of edges in an $F$-free subgraph of $G$. Briggs and Cox introduced a dual version of this problem wherein for a given number $k$, one maximizes the number of edges in a host graph $G$ for which $ex(G,H)

Ilkyoo Choi (최일규), Flexibility of Planar Graphs

Room B232 IBS (기초과학연구원)

Oftentimes in chromatic graph theory, precoloring techniques are utilized in order to obtain the desired coloring result. For example, Thomassen's proof for 5-choosability of planar graphs actually shows that two adjacent vertices on the same face can be precolored. In this vein, we investigate a precoloring extension problem formalized by Dvorak, Norin, and Postle named flexibility. Given a

Paloma T. Lima, Graph Square Roots of Small Distance from Degree One Graphs

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Given a graph class $\mathcal{H}$, the task of the $\mathcal{H}$-Square Root problem is to decide whether an input graph G has a square root H that belongs to $\mathcal{H}$. We are interested in the parameterized complexity of the problem for classes $\mathcal{H}$ that are composed by the graphs at vertex deletion distance at most $k$

Eun Jung Kim (김은정), Solving hard cut problems via flow-augmentation

Room B232 IBS (기초과학연구원)

We present a new technique for designing fixed-parameter algorithms for graph cut problems in undirected graphs, which we call flow augmentation. Our technique is applicable to problems that can be phrased as a search for an (edge) $(s, t)$-cut of cardinality at most $k$ in an undirected graph $G$ with designated terminals s and t.

Akanksha Agrawal, Polynomial Kernel for Interval Vertex Deletion

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Given a graph G and an integer k, the Interval Vertex Deletion (IVD) problem asks whether there exists a vertex subset S of size at most k, such that G-S is an interval graph. A polynomial kernel for a parameterized problem is a polynomial time preprocessing algorithm that outputs an equivalent instance of the problem whose size is bounded by

June Huh (허준이), Kazhdan-Lusztig polynomials of graphs and matroids

Room B232 IBS (기초과학연구원)

I will introduce Kazhdan-Lusztig polynomials of matroids and survey combinatorial and geometric theories built around them. The focus will be on the conjecture of Gedeon, Proudfoot, and Young that all zeros of the Kazhdan-Lusztig polynomial of a matroid lie on the negative real axis.

Robert Ganian, Solving Integer Linear Programs by Exploiting Variable-Constraint Interactions

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Integer Linear Programming (ILP) is among the most successful and general paradigms for solving computationally intractable optimization problems in computer science. ILP is NP-complete, and until recently we have lacked a systematic study of the complexity of ILP through the lens of variable-constraint interactions. This changed drastically in recent years thanks to a series of results that together lay out a