Counting links in complete graphs
Fleming, Thomas ; Mellor, Blake
Osaka J. Math., Tome 46 (2009) no. 1, p. 173-201 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
We find the minimal number of non-trivial links in an embedding of any complete $k$-partite graph on 7 vertices (including $K_{7}$, 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 $k$-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.
Publié le : 2009-03-15
Classification:  05C10,  57M25 
@article{1235574043,
     author = {Fleming, Thomas and Mellor, Blake},
     title = {Counting links in complete graphs},
     journal = {Osaka J. Math.},
     volume = {46},
     number = {1},
     year = {2009},
     pages = { 173-201},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1235574043}
}

Fleming, Thomas; Mellor, Blake. Counting links in complete graphs. Osaka J. Math., Tome 46 (2009) no. 1, pp.  173-201. http://gdmltest.u-ga.fr/item/1235574043/