DC Field | Value | Language |
---|---|---|
dc.contributor.author | Kanté, Mamadou Moustapha | ko |
dc.contributor.author | Kim, Eun Jung | ko |
dc.contributor.author | Kwon, O-Joung | ko |
dc.contributor.author | Oum, Sang-il | ko |
dc.date.accessioned | 2022-10-06T08:00:38Z | - |
dc.date.available | 2022-10-06T08:00:38Z | - |
dc.date.created | 2022-09-27 | - |
dc.date.issued | 2022-03 | - |
dc.identifier.citation | 39th International Symposium on Theoretical Aspects of Computer Science, STACS 2022 | - |
dc.identifier.issn | 1868-8969 | - |
dc.identifier.uri | http://hdl.handle.net/10203/298893 | - |
dc.description.abstract | Every minor-closed class of matroids of bounded branch-width can be characterized by a minimal list of excluded minors, but unlike graphs, this list could be infinite in general. However, for each fixed finite field F, the list contains only finitely many F-representable matroids, due to the well-quasi-ordering of F-representable matroids of bounded branch-width under taking matroid minors [J. F. Geelen, A. M. H. Gerards, and G. Whittle (2002)]. But this proof is non-constructive and does not provide any algorithm for computing these F-representable excluded minors in general. We consider the class of matroids of path-width at most k for fixed k. We prove that for a finite field F, every F-representable excluded minor for the class of matroids of path-width at most k has at most 2|F|O(k2) elements. We can therefore compute, for any integer k and a fixed finite field F, the set of F-representable excluded minors for the class of matroids of path-width k, and this gives as a corollary a polynomial-time algorithm for checking whether the path-width of an F-represented matroid is at most k. We also prove that every excluded pivot-minor for the class of graphs having linear rank-width at most k has at most 22O(k2) vertices, which also results in a similar algorithmic consequence for linear rank-width of graphs. © Mamadou Moustapha Kanté, Eun Jung Kim, O-joung Kwon, and Sang-il Oum. | - |
dc.language | English | - |
dc.publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing | - |
dc.title | Obstructions for Matroids of Path-Width at most k and Graphs of Linear Rank-Width at most k | - |
dc.type | Conference | - |
dc.identifier.scopusid | 2-s2.0-85127178668 | - |
dc.type.rims | CONF | - |
dc.citation.publicationname | 39th International Symposium on Theoretical Aspects of Computer Science, STACS 2022 | - |
dc.identifier.conferencecountry | FR | - |
dc.identifier.conferencelocation | Virtual | - |
dc.identifier.doi | 10.4230/LIPIcs.STACS.2022.40 | - |
dc.contributor.localauthor | Oum, Sang-il | - |
dc.contributor.nonIdAuthor | Kanté, Mamadou Moustapha | - |
dc.contributor.nonIdAuthor | Kim, Eun Jung | - |
dc.contributor.nonIdAuthor | Kwon, O-Joung | - |
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