Counting Links in Complete Graphs

Authors

Thomas Fleming
Blake Mellor, Loyola Marymount UniversityFollow

Document Type

Article

Publication Date

2009

Abstract

We find the minimal number of non-trivial links in an embedding of any complete kk-partite graph on 7 vertices (including K₇, which has at least 21 non-trivial links). We give either exact values or upper and lower bounds for the minimal number of non-trivial links for all complete kk-partite graphs on 8 vertices. We also look at larger complete bipartite graphs, and state a conjecture relating minimal linking embeddings with minimal book embeddings.

Original Publication Citation

Fleming, T. and B. Mellor, 2009: Counting links in complete graphs, Osaka J. Math. 46, 173--201, http://projecteuclid.org/euclid.ojm/1235574043.

Digital Commons @ LMU & LLS Citation

Fleming, Thomas and Mellor, Blake, "Counting Links in Complete Graphs" (2009). Mathematics, Statistics and Data Science Faculty Works. 21.
https://digitalcommons.lmu.edu/math_fac/21