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Journal of Combinatorial Theory Series B
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Journal of Combinatorial Theory Series B
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Grids and their minors

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1989 English Publisher:Elsevier BVJournal:Journal of Combinatorial Theory, Series B, volume 47, pages 349-360 (issn: 0095-8956, Copyright policy )
Authors: W. Wessel; D. G. Seese;

doi: 10.1016/0095-8956(89)90033-6

Grids and their minors

Abstract

We define graphs \(Y_ n\) such that none of these \(Y_ n\) has a minor isomorphic to \(K_ 8\) and for every number k and surface S not all of these graphs are in the completion of k-vertex extensions of graphs embeddable in S. This disproves a corresponding conjecture of \textit{N. Robertson} and \textit{P. D. Seymour} [Graph width and well-quasi-ordering: a survey, Progress in Graph Theory, Proc. Conf. Combinatorics, Waterloo/Ont. 1982, 399-406 (1984; Zbl 0566.05052)].

Keywords

graphs, minor, Computational Theory and Mathematics, surface, Discrete Mathematics and Combinatorics, Planar graphs; geometric and topological aspects of graph theory, Theoretical Computer Science

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Average
Top 10%
Average
hybrid