DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2017-2018): c. 84%

Discussiones Mathematicae Graph Theory

Article in press


Authors:

D. Offner, K. Ojakian

Title:

Capture-time extremal cop-win graphs

Source:

Discussiones Mathematicae Graph Theory

Received: 2017-11-27, Revised: 2019-03-19, Accepted: 2019-03-19, https://doi.org/10.7151/dmgt.2224

Abstract:

We investigate extremal graphs related to the game of Cops and Robbers. We focus on graphs where a single cop can catch the robber; such graphs are called cop-win. The capture time of a cop-win graph is the minimum number of moves the cop needs to capture the robber. We consider graphs that are extremal with respect to capture time, i.e., their capture time is as large as possible given their order. We give a new characterization of the set of extremal graphs. For our alternative approach we assign a rank to each vertex of a graph, and then study which configurations of ranks are possible. We partially determine which configurations are possible, enough to prove some further extremal results. We leave a full classification as an open question.

Keywords:

pursuit-evasion games, cops and robbers, cop-win graphs, capture time, extremal graphs

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