Abstract
It is well known that boundedness of tree-width implies polynomial-time solvability of many algorithmic graph problems. The converse statement is generally not true, i.e., polynomial-time solvability does not necessarily imply boundedness of tree-width. However, in graphs of bounded vertex degree, for some problems, the two concepts behave in a more consistent way. In the present paper, we study this phenomenon with respect to three important graph problems – dominating set, independent dominating set and induced matching – and obtain several results toward revealing the equivalency between boundedness of the tree-width and polynomial-time solvability of these problems in bounded degree graphs.
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Lozin, V., Milanič, M. (2007). Tree-Width and Optimization in Bounded Degree Graphs. In: Brandstädt, A., Kratsch, D., Müller, H. (eds) Graph-Theoretic Concepts in Computer Science. WG 2007. Lecture Notes in Computer Science, vol 4769. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74839-7_5
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DOI: https://doi.org/10.1007/978-3-540-74839-7_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74838-0
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