Grids and their minors
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)].
scientific article; zbMATH DE number 4035859
scientific article