\(p\)-competition graphs
type: Item
instance of: scholarly article
title: \(p\)-competition graphs
zbMATH Open document ID: 0824.05027
DOI: 10.1016/0024-3795(94)00060-Q
author: Suh-Ryung Kim
author: Terry A. McKee
author: F. R. McMorris
author: Fred Roberts
published in: Linear Algebra and its Applications
publication date: 1995-06-12T00:00:00Z
review text: The \(p\)-competition graph of a digraph \(D= (V, A)\) is the graph with vertex set \(V\) and an edge between \(x\) and \(y\) whenever there exist distinct vertices \(v_ 1, v_ 2,\dots, v_ p\) and arcs \((x, v_ i)\), \((y,v_ i)\) in \(D\) for each \(i\leq p\). In case \(p= 1\) the concept coincides with the competition graph which has received a great deal of attention in the literature since being introduced by J. E. Cohen in 1968, see, e.g., \textit{R. D. Dutton} and \textit{R. C. Brigham} [A characterization of competition graphs, Discrete Appl. Math. 6, 315-317 (1983; Zbl 0521.05057)]. In the present paper, the authors study properties of \(p\)-competition graphs, obtaining, where possible, analogues of results about ordinary competition graphs.
Mathematics Subject Classification ID: 05C20
zbMATH DE Number: 754004
zbMATH Keywords: digraph
zbMATH Keywords: competition graph
reviewed by: Martin Škoviera
MaRDI profile type: Publication
cites work: Q4712024
cites work: Q5422499
cites work: Some recent results on niche graphs
cites work: Q4301914
cites work: Niche graphs
cites work: The \(p\)-intersection number of a complete bipartite graph and orthogonal double coverings of a clique
cites work: On rigid circuit graphs
cites work: A characterization of competition graphs
cites work: Niche numbers
cites work: Competition graphs and clique dimensions
cites work: \((i,j)\) competition graphs
cites work: 2-Competition Graphs
cites work: On the p-Edge Clique over Nuber of Complete Bipartite Graphs
cites work: Q4873748
cites work: General results on tolerance intersection graphs
cites work: The 2‐intersection number of paths and bounded‐degree trees
cites work: Q3797197
cites work: \(p\)-competition numbers
cites work: Q3113198
cites work: Q3479858
cites work: A characterization of graphs of competition number m
cites work: Q5284090
cites work: Q3991256
cites work: Some uniqueness results for upper bound graphs
cites work: Q3039403
cites work: Q3689222
cites work: Q4171826
cites work: Q3338254
cites work: Applications of edge coverings by cliques
cites work: A characterization of competition graphs of arbitrary digraphs
cites work: The competition-common enemy graph of a digraph
cites work: The double competition number of some triangle-free graphs
full work available at URL: 0024-3795(94)00060-q
OpenAlex ID: W2066793592
description: scientific article; zbMATH DE number 754004