Intrinsically spherical 3-linked graphs

2021/07/19 by Madeleine Burkhart, Andrew Castillo, Burkhart, Madeleine +7
Computer Science · Engineering · Mathematics · #05C62 (Primary) #57M15 (Secondary) #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Structural Analysis and Optimization #math.CO #msc:05C62 #msc:57M15

paper · pdf · doi:10.48550/arxiv.2107.08953

24 pages, 54 figures

arxiv created 2021/07/19 · openalex publication_date 2021/07/19 · arxiv updated 2021/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We exhibit several families of planar graphs that are minor-minimal intrinsically spherical 3-linked. A graph is intrinsically spherical 3-linked if it is planar graph that has, in every spherical embedding, a non-split 3-link consisting of two disjoint cycles (S¹s) and two disjoint vertices (S⁰), or a cycle and two pairs of disjoint vertices. We conjecture that K₄ \bigcup K₄, K_3,2 \bigcup K_3,2, and K₄ \bigcup K_3,2 form the complete set of minor-minimal intrinsically type I spherical 3-linked graphs (that is, in every spherical embedding, have a nonsplit link of two cycles and one S⁰).

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