On the evaluation at (3,3) of the Tutte polynomial of a graph
type: Item
instance of: scholarly article
title: On the evaluation at (3,3) of the Tutte polynomial of a graph
zbMATH Open document ID: 0674.05024
DOI: 10.1016/0095-8956(88)90079-2
author: Michel Las Vergnas
published in: Journal of Combinatorial Theory. Series B
publication date: 1988-01-01T00:00:00Z
review text: The evaluation t(G;3,3) at (3,3) of the Tutte Polynomial (formerly called the dichromatic polynomial) of a planar graph G is given a combinatorial interpretation as a summation (over non-negative integers k) involving the numbers of Eulerian orientations of the medial graph H of G having exactly k saddle vertices. A divisibility property for t(G;3,3) is obtained as a corollary. A similar summation expresses the evaluation m(H;3) of the Martin Polynomial for a 4-regular graph H imbedded in an arbitrary surface; a similar corollary is obtained.
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 4103089
zbMATH Keywords: Tutte Polynomial
zbMATH Keywords: dichromatic polynomial
zbMATH Keywords: planar graph
zbMATH Keywords: divisibility property
reviewed by: Arthur T. White
MaRDI profile type: Publication
full work available at URL: 0095-8956(88)90079-2
OpenAlex ID: W2015927509
Wikidata QID: Q29544772
cites work: Q4091969
cites work: Q3926612
cites work: On the Tutte Polynomial of a Morphism of Matroids
cites work: Le Polynôme De Martin D'un Graphe Eulerien
cites work: Remarkable valuation of the dichromatic polynomial of planar multigraphs
cites work: Q4063182
cites work: On the Principal Edge Tripartition of a Graph
description: scientific article; zbMATH DE number 4103089