기초과학연구원 이산수학그룹
Circle graphs are the intersection graphs of chords on a circle; vertices correspond to chords, and two vertices are adjacent if their chords intersect. We prove that every circle graph with clique number k has chromatic number at most $4k^2$. Joint with James Davies.
Let $\mathbb N$ be the set of natural numbers. A set $A\subset \mathbb N$ is called a Sidon set if the sums $a_1+a_2$, with $a_1,a_2\in S$ and $a_1\leq a_2$, are distinct, or equivalently, if \ for every $x,y,z,w\in S$ with $x<y\leq z<w$. We define strong Sidon sets as follows: For a constant $\alpha$ with $0\leq …
An equitable tree-$k$-coloring of a graph is a vertex coloring using $k$ distinct colors such that every color class (i.e, the set of vertices in a common color) induces a forest and the sizes of any two color classes differ by at most one. The minimum integer $k$ such that a graph $G$ is equitably …
A $b$-coloring of a graph $G$ is a proper coloring of its vertices such that each color class contains a vertex that has at least one neighbor in all the other color classes. The $b$-Coloring problem asks whether a graph $G$ has a $b$-coloring with $k$ colors. The $b$-chromatic number of a graph $G$, denoted …
Let $Q_n$ be the $n$-dimensional Hamming cube (hypercube) and $N=2^n$. We prove that the number of maximal independent sets in $Q_n$ is asymptotically $2n2^{N/4}$, as was conjectured by Ilinca and Kahn in connection with a question of Duffus, Frankl and Rödl. The value is a natural lower bound derived from a connection between maximal independent …
An odd $$-factor of a graph is a spanning subgraph $H$ such that for every vertex $v \in V(G)$, $1 \le d_H(v) \le b$, and $d_H(v)$ is odd. For positive integers $r \ge 3$ and $b \le r$, Lu, Wu, and Yang gave an upper bound for the third largest eigenvalue in an $r$-regular graph with even number of …
We discuss how the model theoretic notion of first-order transduction allows to define a notion of structural sparsity, and give some example of applications, like existence of low shrub-depth decompositions for tranductions of bounded expansion classes, characterization of transductions of classes with bounded pathwidth, decompositions of graphs with bounded rank-width into cographs.
Given a finite set of elements $V$ and a family $\mathcal{C}$ of subsets of $V$, the set covering problem is to find a minimum cardinality subset of $V$ intersecting every subset in the family $\mathcal{C}$. The set covering problem, also known as the hitting set problem, admits a simple integer linear programming formulation. The constraint …
Schedule July 22 Monday 10:00-11:00 Introduction, 11:00-12:00 Open Problems July 23 Tuesday 10:00-10:30 Stefan Kratsch, Humboldt-Universität zu Berlin, Germany Elimination Distances, Blocking Sets, and Kernels for Vertex Cover 10:45-11:15 Benjamin Bergougnoux, University Clermont Auvergne, France More applications of the d-neighbor equivalence 11:30-12:00 Yixin Cao, Hong Kong Polytechnic University, China Enumerating Maximal Induced Subgraphs 13:30-14:30 Open Problems …
Invited Speakers Jaehoon Kim (김재훈), KAIST Hong Liu (刘鸿), University of Warwick Abhishek Methuku, IBS Discrete Mathematics Group Péter Pál Pach, Budapest University of Technology and Economics Schedule August 12, Monday 11:00am-12:00pm Jaehoon Kim (김재훈): Tree decompositions of graphs without large bipartite holes 12:00pm-1:30pm Lunch 1:30pm-2:30pm Abhishek Methuku: Bipartite Turán problems for ordered graphs 3:00pm-4:00pm Péter Pál …