Fast searching on cactus graphs

Yuan Xue (), Boting Yang (), Sandra Zilles () and Lusheng Wang ()
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Yuan Xue: University of Regina
Boting Yang: University of Regina
Sandra Zilles: University of Regina
Lusheng Wang: City University of Hong Kong

Journal of Combinatorial Optimization, 2023, vol. 45, issue 3, No 2, 22 pages

Abstract: Abstract The problem of finding the fast search number of a graph is NP-complete. It is challenging even when the graph has very small treewidth. However, it can be much easier to find an optimal fast search strategy for smaller subgraphs with special properties. This observation motivates us to establish relationships between optimal fast search strategies for a graph and its subgraphs although fast searching does not have the subgraph-closed property. In this paper, we introduce the notion of k-combinable graphs and study their properties. We propose a new method for computing the fast search number of k-combinable graphs. As an application of this method, we examine the fast searching for cactus graphs. We investigate the properties of optimal fast search strategies and give a linear time algorithm for computing the fast search number of cactus graphs.

Date: 2023
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DOI: 10.1007/s10878-023-01012-x

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