Publication details
Deciding First Order Properties of Matroids
| Authors | |
|---|---|
| Year of publication | 2012 |
| Type | Article in Periodical |
| Magazine / Source | AUTOMATA, LANGUAGES, AND PROGRAMMING, ICALP 2012, PT II |
| Citation | |
| Description | 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 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 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. |