4 research outputs found
New bounds on maximal linkless graphs
We construct a family of maximal linklessly embeddable graphs on vertices
and edges for all , and another family on vertices and edges for all . The latter significantly
improves the lowest edge-to-vertex ratio for any previously known infinite
family. We construct a family of graphs showing that the class of maximal
linklessly embeddable graphs differs from the class of graphs that are maximal
without a minor studied by L. Jorgensen. We give necessary and sufficient
conditions for when the clique sum of two maximal linklessly embeddable graphs
over , , or is a maximal linklessly embeddable graph, and use
these results to prove our constructions yield maximal linklessly embeddable
graphs.Comment: 13 pages, 8 figure