Competition Graphs and Resource Graphs of Digraphs

Abstract

In this paper we study competition graphs of digraphs of restricted degree.
We introduce the notion of restricted competition numbers of graphs.
We complete the characterization of competition graphs of indegree at most 2 and their restricted competition numbers.
We characterize interval $(2,3)$-graphs and give a recognition algorithm for interval $(2,3)$-digraphs.
We characterize competition graphs and interval competition graphs of digraphs of outdegree at most $2$.
The relationship between restricted competition numbers and ordinary competition numbers are studied for several classes of graphs.