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Parameterized counting of trees, forests and matroid bases

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN: 1611-3349, Vol: 10304 LNCS, Page: 85-98
2017
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Conference Paper Description

We prove #W[1]-hardness of counting (1) trees with k edges in a given graph, (2) forests with k edges in a given graph, and (3) bases of a given matroid of rank (or nullity) k representable over an arbitrary field of characteristic two, where k is the parameter.

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