Huy-Tung Nguyen, The average cut-rank of graphs
Room B232 IBS (기초과학연구원)The cut-rank of a set X of vertices in a graph G is defined as the rank of the X×(V(G)∖X) matrix over the binary field whose (i,j)-entry is 1 if …
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Discrete Math Seminar
Jiseung Kim (김지승), Hardness and concrete security in cryptography
Room B232 IBS (기초과학연구원)Computationally hard problems have been widely used to construct cryptographic primitives such as encryptions, digital signatures. For example, provably secure primitives are based on a reduction from the hardness problems. …
Andreas Holmsen, Fractional Helly and topological complexity
Room B232 IBS (기초과학연구원)The fractional Helly theorem is a simple yet remarkable generalization of Helly's classical theorem on the intersection of convex sets, and it is of considerable interest to extend the fractional Helly …
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 …
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 …
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 …
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 …
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 …
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 …
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 …