Related papers: Competition-common enemy graphs of degree-bounded …
S. -R. Kim and F. S. Roberts (2002) introduced the following conditions $C(p)$ and $C'(p)$ for digraphs as generalizations of the condition for digraphs to be semiorders. The condition $C(p)$ (resp. $C'(p)$) is: For any set $S$ of $p$…
The competition graph of a digraph $D$ is a (simple undirected) graph which has the same vertex set as $D$ and has an edge between two distinct vertices $x$ and $y$ if and only if there exists a vertex $v$ in $D$ such that $(x,v)$ and…
The competition hypergraph $C{\cH}(D)$ of a digraph $D$ is the hypergraph such that the vertex set is the same as $D$ and $e \subseteq V(D)$ is a hyperedge if and only if $e$ contains at least 2 vertices and $e$ coincides with the…
If each vertex of an acyclic digraph has indegree at most $i$ and outdegree at most $j$, then it is called an $(i,j)$ digraph, which was introduced by Hefner~{\it et al.}~(1991). Whereas Hefner~{\it et al.} characterized $(i,j)$ digraphs…
The notion of a competition graph was introduced by J. E. Cohen in 1968. The competition graph C(D) of a digraph $D$ is a (simple undirected) graph which has the same vertex set as D and has an edge between two distinct vertices x and y if…
Let D be an acyclic digraph. The competition graph of D is a graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x,v) and (y,v) are arcs of D. For any graph G, G…
The competition graph of a digraph D is a (simple undirected) graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x,v) and (y,v) are arcs of D. For any graph G, G…
The competition graph of a digraph D is a (simple undirected) graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x,v) and (y,v) are arcs of D. For any graph G, G…
The niche graph of a digraph $D$ is the (simple undirected) graph which has the same vertex set as $D$ and has an edge between two distinct vertices $x$ and $y$ if and only if $N^+_D(x) \cap N^+_D(y) \neq \emptyset$ or $N^-_D(x) \cap…
The competition graph of a doubly partial order is known to be an interval graph. The CCE graph and the niche graph of a doubly partial order are also known to be interval graphs if the graphs do not contain a cycle of length four and three…
We say that a digraph $D$ is $(i,j)$-step competitive if any two vertices have an $(i,j)$-step common out-neighbor in $D$ and that a graph $G$ is $(i,j)$-step competitively orientable if there exists an $(i,j)$-step competitive orientation…
An acyclic digraph in which every vertex has indegree at most $i$ and outdegree at most $j$ is called an $(i,j)$ digraph for some positive integers $i$ and $j$. The phylogeny graph of a digraph $D$ has $V(D)$ as the vertex set and an edge…
The competition graph of a digraph D is a graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x,v) and (y,v) are arcs of D. For any graph G, G together with…
The notion of p-competition graphs of digraphs was introduced by S-R. Kim, T. A. McKee, F. R. McMorris, and F. S. Roberts [p-competition graphs, Linear Algebra Appl., 217 (1995) 167--178] as a generalization of the competition graphs of…
The notion of a competition graph was introduced by J. E. Cohen in 1968. The competition graph C(D) of a digraph D is a (simple undirected) graph which has the same vertex set as D and has an edge between two distinct vertices x and y if…
We say that a digraph $D$ is competitive if any pair of vertices has a common out-neighbor in $D$ and that a graph $G$ is competitively orientable if there exists a competitive orientation of $G$. The notion of competitive digraphs arose…
Given an acyclic digraph $D$, the competition graph of $D$, denoted by $C(D)$, is the simple graph having vertex set $V(D)$ and edge set $\{uv \mid (u, w), (v, w) \in A(D) \text{ for some } w \in V(D) \}$. The phylogeny graph of an acyclic…
The competition graph of a directed acyclic graph D is the undirected graph on the same vertex set as D in which two distinct vertices are adjacent if they have a common out-neighbor in D. The competition number of an undirected graph G is…
Competition graphs were created in connected to a biological model as a means of reflecting the competition relations among the predators in the food webs and determining the smallest dimension of ecological phase space. In 2011, Factor and…
A digraph $D$ is an oriented graph if $D$ does not have a pair of opposite arcs. The degree of a vertex $v$ of $D$ is the sum of the in-degree and out-degree of $v.$ Let $fvs(D)$ be the minimum number of vertices whose deletion from $D$…