기초과학연구원 이산수학그룹
I am going to present an algorithm for computing a feedback vertex set of a unit disk graph of size k, if it exists, which runs in time $2^{O(\sqrt{k})}(n + …
The Gyárfás-Sumner conjecture says that for every forest $H$, there is a function $f$ such that the chromatic number $\chi(G)$ is at most $f(\omega(G))$ for every $H$-free graph $G$ ("$H$-free" means with …
Majority dynamics on a graph $G$ is a deterministic process such that every vertex updates its $\pm 1$-assignment according to the majority assignment on its neighbor simultaneously at each step. …
Bouchet (1987) defined delta-matroids by relaxing the base exchange axiom of matroids. Oum (2009) introduced a graphic delta-matroid from a pair of a graph and its vertex subset. We define …
A family $\mathcal F$ of subsets of {1,2,…,n} is called maximal k-wise intersecting if every collection of at most k members from $\mathcal F$ has a common element, and moreover, …
The independence number of a tree decomposition $\mathcal{T}$ of a graph is the smallest integer $k$ such that each bag of $\mathcal{T}$ induces a subgraph with independence number at most …
A well-known theorem of Whitney states that a 3-connected planar graph admits an essentially unique embedding into the 2-sphere. We prove a 3-dimensional analogue: a simply-connected 2-complex every link graph …
Matching minors are a specialisation of minors which preserves the existence and elementary structural properties of perfect matchings. They were first discovered as part of the study of the Pfaffian …
The poset Ramsey number $R(Q_{m},Q_{n})$ is the smallest integer $N$ such that any blue-red coloring of the elements of the Boolean lattice $Q_{N}$ has a blue induced copy of $Q_{m}$ …
Branchwidth determines how graphs, and more generally, arbitrary connectivity (basically symmetric and submodular) functions could be decomposed into a tree-like structure by specific cuts. We develop a general framework for …