Abstract
Graph complexity measures like tree-width, clique-width, NLC-width and rank-width are important because they yield Fixed Parameter Tractable algorithms. Rank-width is based on ranks of adjacency matrices of graphs over GF(2). We propose here algebraic operations on graphs that characterize rank-width. For algorithmic purposes, it is important to represent graphs by balanced terms. We give a unique theorem that generalizes several “balancing theorems” for tree-width and clique-width. New results are obtained for rank-width and a variant of clique-width, called m-clique-width.
Research supported by the french ANR-project Graph decompositions and Algorithms (GRAAL). B. Courcelle is member of Institut Universitaire de France.
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Courcelle, B., Kanté, M.M. (2007). Graph Operations Characterizing Rank-Width and Balanced Graph Expressions. 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_7
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DOI: https://doi.org/10.1007/978-3-540-74839-7_7
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