Vertex-Pursuit in Random Directed Acyclic Graphs
✍ Scribed by Bonato, Anthony; Mitsche, Dieter; Prałat, Paweł
- Book ID
- 120362588
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 2013
- Tongue
- English
- Weight
- 313 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0895-4801
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
A graph G is given and two players, a cop and a robber, play the folioking game: the cop chooses a vertex, then the robber chooses a vertex, then the players move alternately beginning with the cop. A move consists of staying at one's present vertex or moving to an adjacent vertex; each move is seen
Let a random directed acyclic graph be defined as being obtained from the random graph G n p by orienting the edges according to the ordering of vertices. Let γ \* n be the size of the largest (reflexive, transitive) closure of a vertex. For p = c log n /n, we prove that, with high probability, γ \*