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

Neil Robertson; P. D. Seymour

doi:10.1016/0095-8956(90)90120-O

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

Neil Robertson
, P. D. Seymour

Research output: Contribution to journal › Article › peer-review

110 Scopus citations

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 G_i is isomorphic to a minor of G_j. 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.

Original language	English (US)
Pages (from-to)	227-254
Number of pages	28
Journal	Journal of Combinatorial Theory, Series B
Volume	48
Issue number	2
DOIs	https://doi.org/10.1016/0095-8956(90)90120-O
State	Published - Apr 1990
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/0095-8956(90)90120-O

Cite this

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title = "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.",

author = "Neil Robertson and Seymour, \{P. D.\}",

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year = "1990",

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AU - Robertson, Neil

AU - Seymour, P. D.

N1 - Funding Information: *Research partially supported by NSF grant number MCS 8103440

PY - 1990/4

Y1 - 1990/4

N2 - 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.

AB - 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.

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ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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