기초과학연구원 이산수학그룹
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 …
What is the largest number $f(d)$ where every graph with average degree at least $d$ contains a subdivision of $K_{f(d)}$? Mader asked this question in 1967 and $f(d) = \Theta(\sqrt{d})$ …
The independent domination number of a graph $G$, denoted $i(G)$, is the minimum size of an independent dominating set of $G$. In this talk, we prove a series of results regarding …
I will discuss various results for rainbow matching problems. In particular, I will introduce a ‘sampling trick’ which can be used to obtain short proofs of old results as well …