Lattice Path Bicircular Matroids

Lattice Path Bicircular Matroids

Lattice path matroids and bicircular matroids are two well-known classes of transversal matroids. In the seminal work of Bonin and de Mier about structural properties of lattice path matroids, the authors claimed that lattice path matroids significantly differ from bicircular matroids. Recently, it...

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Veröffentlicht in:Graphs and combinatorics 2024-04, Vol.40 (2), Article 21
Hauptverfasser: Guzmán-Pro, Santiago, Hochstättler, Winfried
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Circuits
Combinatorics
Engineering Design
Mathematics
Mathematics and Statistics
Original Paper
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description Lattice path matroids and bicircular matroids are two well-known classes of transversal matroids. In the seminal work of Bonin and de Mier about structural properties of lattice path matroids, the authors claimed that lattice path matroids significantly differ from bicircular matroids. Recently, it was proved that all cosimple lattice path matroids have positive double circuits, while it was shown that there is a large class of cosimple bicircular matroids with no positive double circuits. These observations support Bonin and de Miers’ claim. Finally, Sivaraman and Slilaty suggested studying the intersection of lattice path matroids and bicircular matroids as a possibly interesting research topic. In this work, we exhibit the excluded bicircular matroids for the class of lattice path matroids, and we propose a characterization of the graph family whose bicircular matroids are lattice path matroids. As an application of this characterization, we propose a geometric description of 2-connected lattice path bicircular matroids.
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subjects Circuits
Combinatorics
Engineering Design
Mathematics
Mathematics and Statistics
Original Paper
title Lattice Path Bicircular Matroids
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