Intrinsically triple-linked graphs in RP^3

Abstract

Flapan--Naimi--Pommersheim showed that every spatial embedding of $K_{10}$, the complete graph on ten vertices, contains a non-split three-component link; that is, $K_{10}$ is intrinsically triple-linked in ${\mathbb{R}}^3$. The work of Bowlin--Foisy and Flapan--Foisy--Naimi--Pommersheim extended the list of known intrinsically triple-linked graphs in ${\mathbb{R}}^3$ to include several other families of graphs. In this paper, we will show that while some of these graphs can be embedded 3-linklessly in $\mathbb{R}{P}^3$, $K_{10}$ is intrinsically triple-linked in $\mathbb{R}{P}^3$.

23 pages, 6 figures; v2: revised introduction, minor corrections, new outlines to longer proofs

References in corpus (3)

• Intrinsic knotting and linking of complete graphs
• Intrinsic linking and knotting of graphs in arbitrary 3-manifolds
• Intrinsically Linked Graphs in Projective Space