Vertex-pursuit in random directed acyclic graphs
Combinatorics
2013-08-16 v1
Abstract
We examine a dynamic model for the disruption of information flow in hierarchical social networks by considering the vertex-pursuit game Seepage played in directed acyclic graphs (DAGs). In Seepage, agents attempt to block the movement of an intruder who moves downward from the source node to a sink. The minimum number of such agents required to block the intruder is called the green number. We propose a generalized stochastic model for DAGs with given expected total degree sequence. Seepage and the green number is analyzed in stochastic DAGs in both the cases of a regular and power law degree sequence. For each such sequence, we give asymptotic bounds (and in certain instances, precise values) for the green number.
Cite
@article{arxiv.1308.3380,
title = {Vertex-pursuit in random directed acyclic graphs},
author = {Anthony Bonato and Dieter Mitsche and P. Pralat},
journal= {arXiv preprint arXiv:1308.3380},
year = {2013}
}