Ilkyoo Choi

activity

20132026

most citedStrong edge-colorings of sparse graphs with large maximum degree

17 citations · 116 across the 43 of their papers we have counts for

collaborators

Showing 2020Show all

8 papers · 1 filter

math.CO2020

Improvements on Hippchen's Conjecture

Eun-Kyung Cho, Ilkyoo Choi, Boram Park

Let $G$ be a $k$ -connected graph on $n$ vertices. Hippchen's Conjecture states that two longest paths in $G$ share at least $k$ vertices. Gutiérrez recently proved the conjecture w…

math.CO2020

Decomposing planar graphs into graphs with degree restrictions

Eun-Kyung Cho, Ilkyoo Choi, Ringi Kim +3

Given a graph $G$ , a decomposition of $G$ is a partition of its edges. A graph is $(d, h)$ -decomposable if its edge set can be partitioned into a $d$ -degenerate graph and a graph w…

math.CO2020★ 1 cited

The layer number of $α$ -evenly distributed point sets

Ilkyoo Choi, Weonyoung Joo, Minki Kim

For a finite point set in $R^{d}$ , we consider a peeling process where the vertices of the convex hull are removed at each step. The layer number $L (X)$ of a given point set…

cs.DM2020★ 5 cited

Flexibility of Planar Graphs -- Sharpening the Tools to Get Lists of Size Four

Ilkyoo Choi, Felix Christian Clemen, Michael Ferrara +3

A graph where each vertex $v$ has a list $L (v)$ of available colors is $L$ -colorable if there is a proper coloring such that the color of $v$ is in $L (v)$ for each $v$ . A graph is…

math.CO2020★ 1 cited

The strong clique number of graphs with forbidden cycles

Eun-Kyung Cho, Ilkyoo Choi, Ringi Kim +1

Given a graph $G$ , the strong clique number of $G$ , denoted $ω_{S} (G)$ , is the maximum size of a set $S$ of edges such that every pair of edges in $S$ has distance at most $2$ in the…

math.CO2020

Partitioning planar graphs without $4$ -cycles and $5$ -cycles into bounded degree forests

Eun-Kyung Cho, Ilkyoo Choi, Boram Park

In 1976, Steinberg conjectured that planar graphs without $4$ -cycles and $5$ -cycles are $3$ -colorable. This conjecture attracted numerous researchers for about 40 years, until it w…

math.CO2020★ 1 cited

Generalized list colouring of graphs

Eun-Kyung Cho, Ilkyoo Choi, Yiting Jiang +4

This paper disproves a conjecture of Wang, Wu, Yan and Xie, and answers in negative a question in Dvorak, Pekarek and Sereni. In return, we pose five open problems.

math.CO2020

A sharp Ore-type condition for a connected graph with no induced star to have a Hamiltonian path

Ilkyoo Choi, Jinha Kim

We say a graph $G$ has a Hamiltonian path if it has a path containing all vertices of $G$ . For a graph $G$ , let $σ_{2} (G)$ denote the minimum degree sum of two nonadjacent vertices o…

Improvements on Hippchen's Conjecture

Decomposing planar graphs into graphs with degree restrictions

The layer number of α-evenly distributed point sets

Flexibility of Planar Graphs -- Sharpening the Tools to Get Lists of Size Four

The strong clique number of graphs with forbidden cycles

Partitioning planar graphs without 4-cycles and 5-cycles into bounded degree forests

Generalized list colouring of graphs

A sharp Ore-type condition for a connected graph with no induced star to have a Hamiltonian path

The layer number of $α$ -evenly distributed point sets

Partitioning planar graphs without $4$ -cycles and $5$ -cycles into bounded degree forests