Counting Links in Complete Graphs

Details Counting Links in Complete Graphs Counting Links in Complete Graphs

2006-11-21

arxiv.org/abs/math/0611626v1

Osaka J. Math., vol. 46, 2009, pp. 1-29

Mathematics

Combinatorics

21 pages, several figures

Scientific paper

We find the minimal number of links in an embedding of any complete $k$-partite graph on 7 vertices (including $K_7$, which has at least 21 links). We give either exact values or upper and lower bounds for the minimal number of links for all complete $k$-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.

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