47 citations · 678 across the 85 of their papers we have counts for
8 papers · 1 filter
A polynomial kernel for -leaf power deletion
Jungho Ahn, Eduard Eiben, O-joung Kwon +1
For a non-negative integer , the -leaf power of a tree is a simple graph on the leaves of such that two vertices are adjacent in if and only if their di…
Obstructions for bounded shrub-depth and rank-depth
O-joung Kwon, Rose McCarty, Sang-il Oum +1
Shrub-depth and rank-depth are dense analogues of the tree-depth of a graph. It is well known that a graph has large tree-depth if and only if it has a long path as a subgraph. We…
Equitable partition of planar graphs
Ringi Kim, Sang-il Oum, Xin Zhang
An equitable -partition of a graph is a collection of induced subgraphs of such that is a partition of and…
Graphs of bounded depth- rank-brittleness
O-joung Kwon, Sang-il Oum
We characterize classes of graphs closed under taking vertex-minors and having no and no disjoint union of copies of the -subdivision of for some . Our ch…
The average cut-rank of graphs
Huy-Tung Nguyen, Sang-il Oum
The cut-rank of a set of vertices in a graph is defined as the rank of the matrix over the binary field whose -entry is if the vert…
Branch-depth: Generalizing tree-depth of graphs
Matt DeVos, O-joung Kwon, Sang-il Oum
We present a concept called the branch-depth of a connectivity function, that generalizes the tree-depth of graphs. Then we prove two theorems showing that this concept aligns clos…
Obstructions for partitioning into forests and outerplanar graphs
Ringi Kim, Sergey Norin, Sang-il Oum
For a class of graphs, we define -edge-brittleness of a graph as the minimum such that the vertex set of can be partitioned into sets induci…
Online Ramsey theory for a triangle on -free graphs
Hojin Choi, Ilkyoo Choi, Jisu Jeong +1
Given a class of graphs and a fixed graph , the online Ramsey game for on is a game between two players Builder and Painter as follows: an unbound…