6 papers · 1 filter
Existence of cycles of length divisible by 3 or 4
Ilkyoo Choi, Hojin Chu, Ringi Kim +1
Dean conjectured that for each integer , every graph with minimum degree at least has a cycle whose length is divisible by ; this conjecture is known to be true for…
Competition-common enemy graphs of degree-bounded digraphs
Myungho Choi, Hojin Chu, Suh-Ryung Kim
The competition-common enemy graph (CCE graph) of a digraph is the graph with the vertex set and an edge if and only if and have a common predator and a com…
Digraphs in which every vertices share exactly out-neighbors and exactly in-neighbors
Hojin Chu, Suh-Ryung Kim
In this paper, we introduce the notion of two-way -liking digraphs as a way to extend the results for generalized friendship graphs. A two-way -liking digraph is a di…
Digraphs in which every vertices have exactly common out-neighbors
Myungho Choi, Hojin Chu, Suh-Ryung Kim
We say that a digraph is a -liking digraph if every vertices have exactly common out-neighbors. In 1975, Plesník [Graphs with a homogeneity, 1975. {\it Glasnik Mathe…
Competition graphs of degree bounded digraphs
Hojin Chu, Suh-Ryung Kim
If each vertex of an acyclic digraph has indegree at most and outdegree at most , then it is called an digraph, which was introduced by Hefner~{\it et al.}~(1991). W…
A digraph version of the Friendship Theorem
Myungho Choi, Hojin Chu, Suh-Ryung Kim
The Friendship Theorem states that if in a party any pair of persons has precisely one common friend, then there is always a person who is everybody's friend and the theorem has be…