TY - GEN
T1 - Cops and robber on some families of oriented graphs
AU - Das, Sandip
AU - Gahlawat, Harmender
AU - Sahoo, Uma Kant
AU - Sen, Sagnik
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - Cops and robber game on a directed graph (Formula presented.) initiates by Player 1 placing k cops and then Player 2 placing one robber on the vertices of (Formula presented.). After that, starting with Player 1, alternately the players may move each of their tokens to the adjacent vertices. Player 1 wins if, after a finite number of moves, a cop and the robber end up on the same vertex and Player 2 wins otherwise. However, depending on the type of moves the players make, there are three different models, namely, the normal cop model: both cops and robber move along the direction of the arcs; the strong cop model: cops can move along or against the direction of the arcs while the robber moves along them; and the weak cop model: the robber can move along or against the direction of the arcs while the cops move along them. A graph is cop-win if Player 1 playing with a single cop has a winning strategy. In this article, we study the three models on some families of oriented graphs and characterize the cop-win directed graphs for the third model.
AB - Cops and robber game on a directed graph (Formula presented.) initiates by Player 1 placing k cops and then Player 2 placing one robber on the vertices of (Formula presented.). After that, starting with Player 1, alternately the players may move each of their tokens to the adjacent vertices. Player 1 wins if, after a finite number of moves, a cop and the robber end up on the same vertex and Player 2 wins otherwise. However, depending on the type of moves the players make, there are three different models, namely, the normal cop model: both cops and robber move along the direction of the arcs; the strong cop model: cops can move along or against the direction of the arcs while the robber moves along them; and the weak cop model: the robber can move along or against the direction of the arcs while the cops move along them. A graph is cop-win if Player 1 playing with a single cop has a winning strategy. In this article, we study the three models on some families of oriented graphs and characterize the cop-win directed graphs for the third model.
UR - http://www.scopus.com/inward/record.url?scp=85069658477&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-25005-8_16
DO - 10.1007/978-3-030-25005-8_16
M3 - Conference contribution
AN - SCOPUS:85069658477
SN - 9783030250041
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 188
EP - 200
BT - Combinatorial Algorithms - 30th International Workshop, IWOCA 2019, Proceedings
A2 - Colbourn, Charles J.
A2 - Grossi, Roberto
A2 - Pisanti, Nadia
PB - Springer Verlag
T2 - 30th International Workshop on Combinatorial Algorithms, IWOCA 2019
Y2 - 23 July 2019 through 25 July 2019
ER -