기초과학연구원 이산수학그룹
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 that if $P$ is low-dimensional in some sense (e.g., is defined by intersections of bounded size) then, under polynomial dependencies between $n, k$ and the …
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 studied $F_{k,2}$, and gave bounds when $k=2,3,4,6$ and also in the general case. We study the problem for $d=3$, and provide bounds for $k=2,3,4,6$ and …
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 insertions and deletions. The amortized update time of our data structure is $2^{O(k)} \log n$, where n is the number of vertices. The data structure …
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 in terms of its pfaffians. As a corollary of the new cryptomorphism, we deduce that each component of the orthogonal Grassmannian is parameterized by certain …