14 citations · 118 across the 38 of their papers we have counts for
6 papers · 1 filter
Improvements on Hippchen's Conjecture
Eun-Kyung Cho, Ilkyoo Choi, Boram Park
Let be a -connected graph on vertices. Hippchen's Conjecture states that two longest paths in share at least vertices. Gutiérrez recently proved the conjecture w…
Decomposing planar graphs into graphs with degree restrictions
Eun-Kyung Cho, Ilkyoo Choi, Ringi Kim +3
Given a graph , a decomposition of is a partition of its edges. A graph is -decomposable if its edge set can be partitioned into a -degenerate graph and a graph w…
The strong clique number of graphs with forbidden cycles
Eun-Kyung Cho, Ilkyoo Choi, Ringi Kim +1
Given a graph , the strong clique number of , denoted , is the maximum size of a set of edges such that every pair of edges in has distance at most in the…
Partitioning planar graphs without -cycles and -cycles into bounded degree forests
Eun-Kyung Cho, Ilkyoo Choi, Boram Park
In 1976, Steinberg conjectured that planar graphs without -cycles and -cycles are -colorable. This conjecture attracted numerous researchers for about 40 years, until it w…
The optimal proper connection number of a graph with given independence number
Shinya Fujita, Boram Park
An edge-colored connected graph is properly connected if between every pair of distinct vertices, there exists a path that no two adjacent edges have a same color. Fujita (2019…
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.