Related papers: The double competition multigraph of a digraph
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…
Comparability graphs are a popular class of graphs. We introduce as the digraph analogue of comparability graphs the class of comparability digraphs. We show that many concepts such as implication classes and the knotting graph for a…
In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…
A digraph is semicomplete multipartite if its underlying graph is a complete multipartite graph. As a special case of semicomplete multipartite digraphs, J{\o}rgensen et al. \cite{JG14} initiated the study of doubly regular team…
In this paper, we study the competition graphs of $d$-partial orders and obtain their characterization which extends results given by Cho and Kim \cite{chokim} in 2005. We also show that any graph can be made into the competition graph of a…
In this paper, we study the competition graphs of $d$-partial orders and obtain their characterization which extends results given by Cho and Kim \cite{chokim} in 2005. We also show that any graph can be made into the competition graph of a…
The competition number k(G) of a graph G is the smallest number k such that G together with k isolated vertices added is the competition graph of an acyclic digraph. A chordless cycle of length at least 4 of a graph is called a hole of the…
The competition-common enemy graph (CCE graph) of a digraph $D$ is the graph with the vertex set $V(D)$ and an edge $uv$ if and only if $u$ and $v$ have a common predator and a common prey in $D$. If each vertex of a digraph $D$ has…
It is well known that a plane graph is Eulerian if and only if its geometric dual is bipartite. We extend this result to partial duals of plane graphs. We then characterize all bipartite partial duals of a plane graph in terms of oriented…
In this paper, we compute competition indices and periods of multipartite tournaments. We first show that the competition period of an acyclic digraph $D$ is one and $\zeta(D) +1$ is a sharp upper bound of the competition index of $D$ where…
In this paper, we study $(1,2)$-step competition graphs of bipartite tournaments. A bipartite tournament means an orientation of a complete bipartite graph. We show that the $(1,2)$-step competition graph of a bipartite tournament has at…
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…
The existence of an on-line competitive algorithm for coloring bipartite graphs remains a tantalizing open problem. So far there are only partial positive results for bipartite graphs with certain small forbidden graphs as induced…
The bipartition polynomial of a graph is a generalization of many other graph polynomials, including the domination, Ising, matching, independence, cut, and Euler polynomial. We show in this paper that it is also a powerful tool for proving…
For a flexible labeling of a graph, it is possible to construct infinitely many non-equivalent realizations keeping the distances of connected points constant. We give a combinatorial characterization of graphs that have flexible labelings.…
The notion of graph cover, also known as locally bijective homomorphism, is a discretization of covering spaces known from general topology. It is a pair of incidence-preserving vertex- and edge-mappings between two graphs, the…
In this paper we give two characterisations of the class of reflexive graphs admitting distributive lattice polymorphisms and use these characterisations to address the problem of recognition: for a reflexive graph G in which no two…
In this paper, we relate the competition number of a graph to its edge clique cover number by presenting a tight inequality $k(G) \ge \theta_e(G)-|V(G)|+\widetilde{k}(G)$ where $\theta_e(G)$, $k(G)$, and $\widetilde{k}(G)$ are the edge…
The class of intersection bigraphs of unit intervals of the real line whose ends may be open or closed is called a class of mixed unit interval bigraphs. This class of bigraphs is a strict superclass of the class of unit interval bigraphs.…