- Tytuł:
- Capture-Time Extremal Cop-Win Graphs
- Autorzy:
-
Offner, David
Ojakian, Kerry - Powiązania:
- https://bibliotekanauki.pl/articles/32224106.pdf
- Data publikacji:
- 2021-11-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
pursuit-evasion games
cops and robbers
cop-win graphs
capture time
extremal graphs - Opis:
- 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.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2021, 41, 4; 923-948
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł