Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, February 07, 2013, 12:15 pm

Duration: 45 minutes

Location: OAT S15/S16/S17

Speaker: Daniel Graf

The Cops and Robbers Problem

The game of cops and robbers is played on the vertices of some fixed graph G. Turn by turn one or several cops and a single robber move along the edges of G. The cops win if they capture the robber. The cop number of G is the minimum number of cops needed to win the game.

A long time ago H. Meyniel conjectured that O(n^(1/2)) cops are enough for any connected G on n vertices. M. Aigner and M. Fromme showed that 3 cops are enough for any planar graph. A recent upper bound for general graphs by A. Scott and B. Sudakov improves on several previous results.

In this talk I present an analysis of the game with a single cop as well as several lower and upper bounds on the cop number.

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