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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Excluding infinite trees


Authors: P. D. Seymour and Robin Thomas
Journal: Trans. Amer. Math. Soc. 335 (1993), 597-630
MSC: Primary 05C75; Secondary 03E05, 03E35, 05C05
DOI: https://doi.org/10.1090/S0002-9947-1993-1079058-6
MathSciNet review: 1079058
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Abstract: For each infinite cardinal $ \kappa $ we give several necessary and sufficient conditions for a graph not to contain a minor isomorphic to the infinite $ \kappa $-branching tree in terms of a certain kind of a "tree-decomposition," in terms of a "path-decomposition," and also in terms of a "cops-and-robber game." We also give necessary and sufficient conditions for a graph not to contain a subgraph isomorphic to a subdivision of the same tree.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1079058-6
Article copyright: © Copyright 1993 American Mathematical Society