Disjoint Genus-0 Surfaces in Extremal Graph Theory and Set Theory Lead To a Novel Topological Theorem
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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.
1980 ◽
Vol 29
(3)
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pp. 368-369
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2014 ◽
Vol 24
(4)
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pp. 585-608
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1994 ◽
Vol 68
(2)
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pp. 296-316
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2009 ◽
Vol 18
(3)
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pp. 335-355
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