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From Pathwidth to Connected Pathwidth
It is proven that the connected pathwidth of any graph is at most
2\cdot\pw(G)+1, where \pw(G) is the pathwidth of . The method is
constructive, i.e. it yields an efficient algorithm that for a given path
decomposition of width computes a connected path decomposition of width at
most . The running time of the algorithm is , where is the
number of `bags' in the input path decomposition.
The motivation for studying connected path decompositions comes from the
connection between the pathwidth and the search number of a graph. One of the
advantages of the above bound for connected pathwidth is an inequality
\csn(G)\leq 2\sn(G)+3, where \csn(G) and \sn(G) are the connected search
number and the search number of . Moreover, the algorithm presented in this
work can be used to convert a given search strategy using searchers into a
(monotone) connected one using searchers and starting at an arbitrary
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