Abstract
We establish that a set of finite graphs of tree-width at most k is recognizable (with respect to the algebra of graphs with an unbounded number of sources) if and only if it is recognizable with respect to the algebra of graphs with at most k sources. We obtain a somewhat stronger result for sets of simple finite graphs of tree-width at most k.
Supported by ESPRIT-Basic Research Working group āCOMPUGRAPHā
Supported by the Swedish Natural Science Research Council
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K. Abrahamson and M. Fellows. Finite automata, bounded tree-width and well-quasiordering. In N. Robertson and P. Seymour, editors, Graph Structure Theory. Contemporary Mathematics vol. 147, pages 539ā564. AMS, Providence. Rhode Island, 1993.
S. Arnborg, B. Courcelle, A. Proskurowski, and D. Seese. An algebraic theory of graph reduction. Technical Report LaBRI-90-02, Universite de Bordeaux, Jan. 1990. To appear in JACM, extended abstract in Lec. Notes Comp. Sci. 532:70ā83. 1991.
S. Arnborg, J. Lagergren, and D. Seese. Problems easy for tree-decomposable graphs. J. of Algorithms, 12:308ā340, 1991.
B. Courcelle. The monadic second order logic of graphs I: Recognizable sets of finite graphs. Information and Computation, 85:12ā75, March 1990.
B. Courcelle. The monadic second-order logic of graphs V: On closing the gap between definability and recognizability. Theoret. Comput. Sci. 80:153ā202, 1991.
B. Courcelle. The monadic second-order logic of graphs III: Tree-decompositions. minors and complexity issues. Informatique ThĆ©orique et Applications, 26:257ā286, 1992.
B. Courcelle. Recognizable sets of graphs: equivalent definitions and closure properties. Technical Report 92-06, Bordeaux-1 University, 1992. To appear in Mathematical Structures in Computer Science.
A. Habel, H.J. Kreowski, and C. Lautemann. A comparison of compatible. finite. and inductive graph properties. Theoret. Comput. Sci., 89:33ā62, 1991.
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Ā© 1994 Springer-Verlag Berlin Heidelberg
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Courcelle, B., Lagergren, J. (1994). Recognizable sets of graphs of bounded tree-width. In: Schneider, H.J., Ehrig, H. (eds) Graph Transformations in Computer Science. Lecture Notes in Computer Science, vol 776. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57787-4_9
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DOI: https://doi.org/10.1007/3-540-57787-4_9
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