2021/08/30 by Naimi, Ramin, Odeneal, Ryan, Pavelescu, Andrei +1
#57M25 (Primary) 05C10 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2108.12946
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 K6-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 Verdière invariant for graphs on at most 11 vertices. We give a description of the programs used in the search.