Cops and robber on some families of oriented graphs

Sandip Das, Harmender Gahlawat, Uma Kant Sahoo, Sagnik Sen

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

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.

Original languageEnglish
Title of host publicationCombinatorial Algorithms - 30th International Workshop, IWOCA 2019, Proceedings
EditorsCharles J. Colbourn, Roberto Grossi, Nadia Pisanti
PublisherSpringer Verlag
Pages188-200
Number of pages13
ISBN (Print)9783030250041
DOIs
StatePublished - 1 Jan 2019
Externally publishedYes
Event30th International Workshop on Combinatorial Algorithms, IWOCA 2019 - Pisa, Italy
Duration: 23 Jul 201925 Jul 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11638 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference30th International Workshop on Combinatorial Algorithms, IWOCA 2019
Country/TerritoryItaly
CityPisa
Period23/07/1925/07/19

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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