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• W1636778749 abstract "Frick and Grohe [J. ACM 48 (2006), 1184–1206] introduced a notion of graph classes with locally bounded tree-width and established that every first order logic property can be decided in almost linear time in such a graph class. Here, we introduce an analogous notion for matroids (locally bounded branch-width) and show the existence of a fixed parameter algorithm for first order logic properties in classes of regular matroids with locally bounded branch-width. To obtain this result, we show that the problem of deciding the existence of a circuit of length at most k containing two given elements is fixed parameter tractable for regular matroids." @default.
• W1636778749 created "2016-06-24" @default.
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• W1636778749 date "2011-08-27" @default.
• W1636778749 modified "2023-09-27" @default.
• W1636778749 title "Deciding First Order Logic Properties of Matroids" @default.
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