A characterization of some graph classes using excluded minors
type: Item
instance of: scholarly article
title: A characterization of some graph classes using excluded minors
zbMATH Open document ID: 1164.05057
author: Janka Chlebíková
published in: Periodica Mathematica Hungarica
publication date: 2008-10-22T00:00:00Z
full work available at URL: a-characterization-of-some-graph-classes-using-excluded-minors(2d0aa654-aec2-423e-9e23-c6c40427e653).html
review text: Some structural characterization of graphs with excluded minors are offered. The excluded minors in different combinations are the \(K_{3, 3}\), \(K_5\), the octahedron graph, the prism and some others that came with the small modifications of the previous ones. The author proves a number of results, part of those new, while the others are simplification of already known ones, see e.g. \textit{G. A. Dirac} [Can. Math. Bull. 6, 183-210 (1963; Zbl 0138.19203)]. The proofs are relatively easy, thanks to the use of the ``Wheel theorem'' of \textit{W. T. Tutte} [Nederl. Akad. Wet., Proc., Ser. A 64, 441-455 (1961; Zbl 0101.40903)], and its strengthening by \textit{P. D. Seymour} [J. Comb. Theory, Ser. B 28, 305-359 (1980; Zbl 0443.05027)].
reviewed by: András Pluhár
Mathematics Subject Classification ID: 05C75
Mathematics Subject Classification ID: 05C83
zbMATH DE Number: 5355810
zbMATH Keywords: excluded minors
zbMATH Keywords: \(\leq k\)-sum of graphs
zbMATH Keywords: tree width of a graph
MaRDI profile type: Publication
OpenAlex ID: W1972643692
cites work: Forbidden minors characterization of partial 3-trees
cites work: Q3999150
cites work: Some Results Concerning the Structure of Graphs
cites work: Über Minimalstrukturen von Graphen, insbesondere von n-fach zusammenhängenden Graphen
cites work: An excluded minor theorem for the octahedron
cites work: Graph minors. III. Planar tree-width
cites work: A characterization of partial 3-trees
cites work: Decomposition of regular matroids
cites work: Q4263662
cites work: Q3284374
cites work: Bemerkungen zu Hadwigers Vermutung
DOI: 10.1007/S10998-007-3001-4
description: scientific article; zbMATH DE number 5355810