منابع مشابه
A robber locating strategy for trees
The robber locating game, introduced by Seager in [8], is a variation of the classic cops and robbers game on a graph. A cop attempts to locate an invisible robber on a graph by probing a single vertex v each turn, from which the cop learns the robber’s distance. The robber is then permitted to stay at his current vertex or move to an adjacent vertex other than v. A graph is locatable if the co...
متن کاملThe Robber Locating game
In 2012 Seager introduced a new variant of the Cops and Robbers game, in which a cop searches for a moving robber on a graph using distance probes. The robber on his turn can either remain still or move to an adjacent vertex, while the cop on her turn probes any vertex and learns the robber’s distance from the probed vertex. Carraher, Choi, Delcourt, Erickson and West later showed that for any ...
متن کاملLocating a robber on a graph
Consider the following game of a cop locating a robber on a connected graph. At each turn, the cop chooses a vertex of the graph to probe and receives the distance from the probe to the robber. If she can uniquely locate the robber after this probe, then she wins. Otherwise the robber may either stay put or move to any vertex adjacent to his location other than the probe vertex. The cop’s goal ...
متن کاملLocating a robber on a graph via distance queries
A cop wants to locate a robber hiding among the vertices of a graph. A round of the game consists of the robber moving to a neighbor of its current vertex (or not moving) and then the cop scanning some vertex to obtain the distance from that vertex to the robber. If the cop can at some point determine where the robber is, then the cop wins; otherwise, the robber wins. We prove that the robber w...
متن کاملA sharp lower bound for locating-dominating sets in trees
Let LD(G) denote the minimum cardinality of a locating-dominating set for graph G. If T is a tree of order n with l leaf vertices and s support vertices, then a known lower bound of Blidia, Chellali, Maffray, Moncel and Semri [Australas. J. Combin. 39 (2007), 219–232] is LD(T ) ≥ (n+ 1 + l − s)/3 . In this paper, we show that LD(T ) ≥ (n+ 1 + 2(l − s))/3 and these bounds are sharp. We construct...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2017
ISSN: 0166-218X
DOI: 10.1016/j.dam.2017.07.019