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Universality in minor-closed graph classes
[article]

2021
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arXiv
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pre-print

Stanislaw Ulam asked whether there exists a universal countable planar graph (that is, a countable planar graph that contains every countable planar graph as a subgraph). János Pach (1981) answered this question in the negative. We strengthen this result by showing that every countable graph that contains all countable planar graphs must contain (i) an infinite complete graph as a minor, and (ii) a subdivision of the complete graph K_t with multiplicity t, for every finite t. On the other hand,

arXiv:2109.00327v1
fatcat:wmv5mwtfvjfttfhjmxuswpn27e