
A Game of Cops and Robbers on Graphs with Periodic EdgeConnectivity
This paper considers a game in which a single cop and a single robber ta...
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On Computing Centroids According to the pNorms of Hamming Distance Vectors
In this paper we consider the pNorm Hamming Centroid problem which asks...
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On the meternal Domination Number of Cactus Graphs
Given a graph G, guards are placed on vertices of G. Then vertices are s...
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Short rainbow cycles in sparse graphs
Let G be a simple nvertex graph and c be a colouring of E(G) with n col...
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Complexity Issues of String to Graph Approximate Matching
The problem of matching a query string to a directed graph, whose vertic...
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Weighted Shortest Common Supersequence Problem Revisited
A weighted string, also known as a position weight matrix, is a sequence...
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Deciding ωRegular Properties on Linear Recurrence Sequences
We consider the problem of deciding ωregular properties on infinite tra...
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A Timecop's Chase Around the Table
We consider the cops and robber game variant consisting of one cop and one robber on timevarying graphs (TVG). The considered TVGs are edge periodic graphs, i.e., for each edge, a binary string s_e determines in which time step the edge is present, namely the edge e is present in time step t if and only if the string s_e contains a 1 at position t s_e. This periodicity allows for a compact representation of the infinite TVG. We proof that even for very simple underlying graphs, i.e., directed and undirected cycles the problem whether a copwinning strategy exists is NPhard and W[1]hard parameterized by the number of vertices. Our second main result are matching lower bounds for the ratio between the length of the underlying cycle and the least common multiple (LCM) of the lengths of binary strings describing edgeperiodicies over which the graph is robberwinning. Our third main result improves the previously known EXPTIME upper bound for Periodic Cop and Robber on general edge periodic graphs to PSPACEmembership.
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