The Merino–Welsh Conjecture for Split Matroids-Reference-Cited by-同舟云学术

The Merino–Welsh Conjecture for Split Matroids

Published:2022-12-17 Issue: Volume: Page:
ISSN:0218-0006
Container-title:Annals of Combinatorics
language:en
Short-container-title:Ann. Comb.

Author:

Ferroni Luis^ORCID,Schröter Benjamin^ORCID

Abstract

AbstractIn 1999, Merino and Welsh conjectured that evaluations of the Tutte polynomial of a graph satisfy an inequality. In this short article, we show that the conjecture generalized to matroids holds for the large class of all split matroids by exploiting the structure of their lattice of cyclic flats. This class of matroids strictly contains all paving and copaving matroids.

Funder

Swedish Research Council

Knut och Alice Wallenbergs Stiftelse

Publisher

Springer Science and Business Media LLC

Subject

Discrete Mathematics and Combinatorics

Link

https://link.springer.com/content/pdf/10.1007/s00026-022-00628-w.pdf

Reference18 articles.

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2. J. E. Bonin and A. de Mier. The lattice of cyclic flats of a matroid. Ann. Comb., 12(2):155–170, 2008.

3. T. Brylawski and J. Oxley. The Tutte polynomial and its applications. In Matroid applications, volume 40 of Encyclopedia Math. Appl., pages 123–225. Cambridge Univ. Press, Cambridge, 1992.

4. A. Cameron and D. Mayhew. Excluded minors for the class of split matroids. Australas. J. Combin., 79:195–204, 2021.

5. L. E. Chávez-Lomelí, C. Merino, S. D. Noble, and M. Ramírez-Ibáñez. Some inequalities for the Tutte polynomial. European J. Combin., 32(3):422–433, 2011.

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