Treelength of series–parallel graphs
نویسندگان
چکیده
The length of a tree-decomposition graph is the maximum distance (in graph) between two vertices same bag decomposition. treelength minimum among its tree-decompositions. Treelength graphs has been studied for algorithmic applications in classical metric problems such as Traveling Salesman Problem or dimension and also, compact routing context distributed computing. Deciding whether general at most 2 NP-complete (graphs one are precisely chordal graphs), it known that cannot be approximated up to factor less than 32 (the best approximation algorithm an ratio 3). However, nothing on computational complexity planar graphs, except any outerplanar equal third size largest isometric cycle. This work initiates study by considering next natural subclass namely series–parallel graphs. We first fully describe melon (set pairwise internally disjoint paths linking vertices), showing that, even restricted class, expression not trivial. Then, we show can Our main result quadratic-time deciding 2. latter relies characterization with terms infinite family forbidden subgraphs.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2023
ISSN: ['1872-6771', '0166-218X']
DOI: https://doi.org/10.1016/j.dam.2023.07.022