Searching Cycle-Disjoint Graphs
نویسندگان
چکیده
In this paper, we consider the edge searching problem on cycle-disjoint graphs. We first improve the running time of the algorithm to compute the vertex separation and the optimal layout of a unicyclic graph, which is given by Ellis et al. (2004), from O(n log n) to O(n). By a linear-time transformation, we can compute the edge search number of a unicyclic graph in linear time. We also propose an O(n) time algorithm to compute the edge search number and the optimal edge search strategy of a cycle-disjoint graph in which every cycle has at most three vertices with degree more than two. We show how to compute the search number for a k-ary cycle-disjoint graph. We also present some results on approximation algorithms.
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