Graph Decompositions and Monadic Second Order Logic
A tree decomposition is a tool which allows for analysis of the underlying tree structure of graphs which are not trees. Given a class of graphs with bounded tree width, many NP-complete problems can be computed in linear time for graphs in the class. Clique width of a graph G is a measure of the nu...
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Digital WPI
2009
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| Online Access: | https://digitalcommons.wpi.edu/etd-theses/364 https://digitalcommons.wpi.edu/cgi/viewcontent.cgi?article=1363&context=etd-theses |
| Summary: | A tree decomposition is a tool which allows for analysis of the underlying tree structure of graphs which are not trees. Given a class of graphs with bounded tree width, many NP-complete problems can be computed in linear time for graphs in the class. Clique width of a graph G is a measure of the number of labels required to construct G using several particular graph operations. For any integer k, both the class of graphs with tree width at most k and the class of graphs with clique width at most k have a decidable monadic second order theory. In this paper we explore some recent results in applying these graph measures and their relation to monadic second order logic. |
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