The Complement Problem for Linklessly Embeddable Graphs

Ramin Naimi; Ryan Odeneal; Andrei Pavelescu; Elena Pavelescu

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arXiv · 2108.12946

The Complement Problem for Linklessly Embeddable Graphs

Ramin Naimi·Ryan Odeneal·Andrei Pavelescu·Elena Pavelescu

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Abstract

We find all maximal linklessly embeddable graphs of order up to 11, and verify that for every graph $G$ of order 11 either $G$ or its complement $cG$ is intrinsically linked. We give an example of a graph $G$ of order 11 such that both $G$ and $cG$ are $K_6$-minor free. We provide minimal order examples of maximal linklessly embeddable graphs that are not triangular or not 3-connected. We prove a Nordhaus-Gaddum type conjecture on the Colin de Verdi\`ere invariant for graphs on at most 11 vertices. We give a description of the programs used in the search.

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BibTeX RIS

Ramin Naimi, Ryan Odeneal, Andrei Pavelescu, Elena Pavelescu. 2021-08-30. The Complement Problem for Linklessly Embeddable Graphs. https://arxiv.org/abs/2108.12946

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