Theoretical Computer Science
On a pursuit game of Cayley diagraphs
European Journal of Combinatorics
The complexity of searching a graph
Journal of the ACM (JACM)
Monotonicity in graph searching
Journal of Algorithms
Recontamination does not help to search a graph
Journal of the ACM (JACM)
Search and sweep numbers of finite directed acyclic graphs
Discrete Applied Mathematics
On the monotonicity of games generated by symmetric submodular functions
Discrete Applied Mathematics - Submodularity
Digraph searching, directed vertex separation and directed pathwidth
Discrete Applied Mathematics
Directed searching digraphs: monotonicity and complexity
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Arc searching digraphs without jumping
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
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In this paper, we propose and study two digraph searching models: weak searching and mixed weak searching. In these two searching models, each searcher must follow the edge directions when they move along edges, but the intruder can move from tail to head or from head to tail along edges. We prove the monotonicity of the mixed weak searching model by using Bienstock and Seymour's method, and prove the monotonicity of the weak searching model by using LaPaugh's method. We show that both searching problems are NP-complete.