기초과학연구원 이산수학그룹
In 2005, Bollobás, Janson and Riordan introduced and extensively studied a general model of inhomogeneous random graphs parametrised by graphons. In particular, they studied the emergence of a giant component …
An $r$-graph is an $r$-regular graph in which every odd set of vertices is connected to its complement by at least $r$ edges. A central question regarding $r$-graphs is determining …
For a positive real number $p$, the $p$-norm $\|G\|_p$ of a graph $G$ is the sum of the $p$-th powers of all vertex degrees. We study the maximum $p$-norm $\mathrm{ex}_{p}(n,F)$ …
An edge-weighted graph $G$, possibly with loops, is said to be antiferromagnetic if it has nonnegative weights and at most one positive eigenvalue, counting multiplicities. The number of graph homomorphisms …
In 1966, Kleitman established that if \( |A \triangle B| \leq d \) for any \( A, B \in \mathcal{F} \), then \( |\mathcal{F}| \leq \sum_{i=0}^{k} \binom{n}{i} \) for \( …
A major goal of additive combinatorics is to understand the structures of subsets A of an abelian group G which has a small doubling K = |A+A|/|A|. Freiman's celebrated theorem …
The peaceable queens problem asks to determine the maximum number $a(n)$ such that there is a placement of $a(n)$ white queens and $a(n)$ black queens on an $n \times n$ …
A replacement action is a function $\mathcal L$ that maps each graph to a collection of subgraphs of smaller size. Given a graph class $\mathcal H$, we consider a general …
The group \( S_n \) of permutations on \(=\{1,2,\dots,n\} \) is generated by simple transpositions \( s_i = (i,i+1) \). The length \( \ell(\pi) \) of a permutation \( \pi …
An induced packing of cycles in a graph is a set of vertex-disjoint cycles such that the graph has no edge between distinct cycles of the set. The classic Erdős-Pósa theorem …