On p-competition graphs of loopless Hamiltonian digraphs without symmetric arcs and graph operations

For a digraph $D$, the $p$-competition graph $C_{p}(D)$ of $D$ is the graph satisfying the following: $V(C_{p}(D))=V(D)$, for $x,y \in V(C_{p}(D))$, $xy \in E(C_{p}(D))$ if and only if there exist distinct $p$ vertices $v_{1},$ $v_{2},$ $...,$ $v_{p}$ $\in$ $V(D)$ such that $x \rightarrow v_{i}$, $y \rightarrow v_{i}$ $\in$ $A(D)$ for each $i=1,2,$ $...,$ $p$. We show the $H_1 \cup H_2$ is a $p$-competition graph of a loopless digraph without symmetric arcs for $p \geq 2$, where $H_1$ and $H_2$ are $p$-competition graphs of loopless digraphs without symmetric arcs and $V(H_1) \cap V(H_2)$ $=$ $\{ \alpha \}$. For $p$-competition graphs of loopless Hamiltonian digraphs without symmetric arcs, we obtain similar results. And we show that a star $K_{1,n}$ is a $p$-competition graph of a loopless Hamiltonian digraph without symmetric arcs if $n \geq 2p+3$ and $p \geq 3$. Based on these results, we obtain conditions such that spiders, caterpillars and cacti are $p$-competition graphs of loopless digraphs without symmetric arcs. We also obtain conditions such that these graphs are $p$-competition graphs of loopless Hamiltonian digraphs without symmetric arcs

The competition hypergraphs of doubly partial orders

Since Cho and Kim (2005) showed that the competition graph of a doubly partial order is an interval graph, it has been actively studied whether or not the same phenomenon occurs for other variants of competition graph and interesting results have been obtained. Continuing in the same spirit, we study the competition hypergraph, an interesting variant of the competition graph, of a doubly partial order. Though it turns out that the competition hypergraph of a doubly partial order is not always interval, we completely characterize the competition hypergraphs of doubly partial orders which are interval.Comment: 12 pages, 6 figure

The p-Competition Graphs of Strongly Connected and Hamiltonian Digraphs

Competition graphs were first introduced by Joel Cohen in the study of food webs and have been since extensively studied. Graphs which are the competition graph of a strongly connected or Hamiltonian digraph are of particular interest in applications to communication networks.This research was partially supported by Research Contract N00014-91-J-1145 and N00014-93-1-0670 of the Office of Naval Research

Summary of Research 1994

The views expressed in this report are those of the authors and do not reflect the official policy or position of the Department of Defense or the U.S. Government.This report contains 359 summaries of research projects which were carried out under funding of the Naval Postgraduate School Research Program. A list of recent publications is also included which consists of conference presentations and publications, books, contributions to books, published journal papers, and technical reports. The research was conducted in the areas of Aeronautics and Astronautics, Computer Science, Electrical and Computer Engineering, Mathematics, Mechanical Engineering, Meteorology, National Security Affairs, Oceanography, Operations Research, Physics, and Systems Management. This also includes research by the Command, Control and Communications (C3) Academic Group, Electronic Warfare Academic Group, Space Systems Academic Group, and the Undersea Warfare Academic Group