Graph decompositions definable in monadic second-order logic |
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Affiliation: | LaBRI (CNRS), Bordeaux 1 University, 33405 Talence, France |
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Abstract: | We prove that the split decomposition of a graph is definable by Monadic Second-Order formulas. We also prove that the set of graphs having the same cycle matroid as a given graph is definable from this graph by Monadic Second-Order formulas. These results are consequences of general results on the logical definability of graph decompositions of various types. |
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