Note: On the number of connected convex subgraphs of a connected acyclic digraph

Authors:
Gregory Gutin;Anders Yeo
Affiliations:
Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK;Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

A digraph D is connected if the underlying undirected graph of D is connected. A subgraph H of an acyclic digraph D is convex if there is no directed path between vertices of H which contains an arc not in H. We find the minimum and maximum possible number of connected convex subgraphs in a connected acyclic digraph of order n. Connected convex subgraphs of connected acyclic digraphs are of interest in the area of modern embedded processors technology.