Preprint Short Note Version 1 Preserved in Portico This version is not peer-reviewed

Disjoint Genus-0 Surfaces in Extremal Graph Theory and Set Theory Lead To a Novel Topological Theorem

Version 1 : Received: 4 September 2021 / Approved: 6 September 2021 / Online: 6 September 2021 (10:09:59 CEST)

How to cite: Tozzi, A. Disjoint Genus-0 Surfaces in Extremal Graph Theory and Set Theory Lead To a Novel Topological Theorem. Preprints 2021, 2021090082 (doi: 10.20944/preprints202109.0082.v1). Tozzi, A. Disjoint Genus-0 Surfaces in Extremal Graph Theory and Set Theory Lead To a Novel Topological Theorem. Preprints 2021, 2021090082 (doi: 10.20944/preprints202109.0082.v1).

Abstract

When an edge is removed, a cycle graph Cn becomes a n-1 tree graph. This observation from extremal set theory leads us to the realm of set theory, in which a topological manifold of genus-1 turns out to be of genus-0. Starting from these premises, we prove a theorem suggesting that a manifold with disjoint points must be of genus-0, while a manifold of genus-1 cannot encompass disjoint points.

Keywords

Combinatorics; Ramsey’s theory; Borsuk–Ulam theorem; black hole; singularity

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