The Merino–Welsh Conjecture for Split Matroids

In 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.

Metadaten
Author:	Luis Ferroni ORCiD, Benjamin Frederik Schröter ORCiD GND
URN:	urn:nbn:de:hebis:30:3-794156
DOI:	https://doi.org/10.1007/s00026-022-00628-w
Parent Title (English):	Annals of combinatorics
Publisher:	Springer
Document Type:	Article
Language:	English
Date of Publication (online):	2022/12/17
Date of first Publication:	2022/12/17
Publishing Institution:	Universitätsbibliothek Johann Christian Senckenberg
Release Date:	2023/11/02
Volume:	27.2023
Page Number:	12
First Page:	737
Last Page:	748
HeBIS-PPN:	514461349
Institutes:	Informatik und Mathematik / Mathematik
Dewey Decimal Classification:	5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:	05-XX COMBINATORICS (For finite fields, see 11Txx) / 05Bxx Designs and configurations (For applications of design theory, see 94C30) / 05B35 Matroids, geometric lattices [See also 52B40, 90C27]
	05-XX COMBINATORICS (For finite fields, see 11Txx) / 05Cxx Graph theory (For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15) / 05C31 Graph polynomials
Sammlungen:	Universitätspublikationen
Licence (German):	Creative Commons - CC BY - Namensnennung 4.0 International

Open Access