기초과학연구원 이산수학그룹
Given a $k$-uniform hypergraph $F$, its Turán density $\pi(F)$ is the infimum over all $d\in $ such that any $n$-vertex $k$-uniform hypergraph $H$ with at least $d\binom{n}{k}+o(n^k)$ edges contains a …
Consider a general Turan-type problem on hypergraphs. Let $\mathcal{F}$ be a family of $k$-subsets of $$ that does not contain sets $F_1, \ldots, F_s$ satisfying some property $P$. We show …
Let $F_{k,d}(n)$ be the maximal size of a set ${A}\subseteq $ such that the equation \ has no solution with $a_1,a_2,\ldots,a_k\in A$ and integer $x$. Erdős, Sárközy and T. Sós …
Extremely sparse random binary matrices tend to be singular, due to the likely presence of "local combinatorial dependencies" such as all-zero columns or pairs of identical columns. We discuss this …
We present a dynamic data structure that maintains a tree decomposition of width at most 9k+8 of a dynamic graph with treewidth at most k, which is updated by edge …
Given a prime power $q \equiv 1 \pmod 4$, the Paley graph of order $q$ is the graph defined over $\mathbb{F}_q$ (the finite field with $q$ elements), such that two …
We present a new cryptomorphic definition of orthogonal matroids with coefficients using Grassmann-Plücker functions. The equivalence is motivated by Cayley's identities expressing principal and almost-principal minors of a skew-symmetric matrix …
Since the development of the first randomized polynomial-time algorithm for volume computation by Dyer, Frieze, and Kannan in 1989, convex-body sampling has been a central problem at the intersection of …
In , Fabianski et. al. developed a simple, yet surprisingly powerful algorithmic framework to develop efficient parameterized graph algorithms. Notably they derive a simple parameterized algorithm for the dominating set …