The unbreakable quasi-graphic matroids
Sayantani Bhattacharya, John David Clifton, Zach Walsh
TL;DR
This paper characterizes 3-connected unbreakable quasi-graphic matroids, extending previous work on graphic and frame matroids, and includes a specific case for lifted-graphic matroids.
Contribution
It provides a complete characterization of 3-connected unbreakable quasi-graphic matroids, generalizing prior results on related matroid classes.
Findings
Characterization of 3-connected unbreakable quasi-graphic matroids
Extension of previous results on graphic and frame matroids
Special case characterization of 3-connected lifted-graphic matroids
Abstract
A matroid M is unbreakable if it is connected and M/F is connected for every flat F of M . Oxley and Pfeil characterized the unbreakable graphic matroids, and Fife, Mayhew, Oxley, and Semple characterized the graphs underlying 3-connected unbreakable frame matroids. We extend the latter result by giving a complete characterization of the 3-connected unbreakable quasi-graphic matroids. As a special case we obtain a characterization of the 3-connected lifted-graphic matroids.
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