论文信息 - Graph minors. IV. Tree-width and well-quasi-ordering

Graph minors. IV. Tree-width and well-quasi-ordering

Abstract K. Wagner conjectured that if G1, G2, … is any countable sequence of finite graphs, then there exist i, j with j > i ≥ 1 such that Gi is isomorphic to a minor of Gj. Kruskal proved this when G1, G2, … are all trees. We prove a strengthening of Kruskal's result-Wagner's conjecture is true for all sequences in which G1 is planar. We hope to show in a future paper that Wagner's conjecture is true in general, and the results of this paper will be needed for that proof.

Paul D. Seymour | Neil Robertson | P. Seymour | N. Robertson

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