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Maximum number of edges a single edge crosses in a drawing of the complete graph K_n where every vertex lies on the outer face.
0

%I #11 Jun 25 2022 17:07:13

%S 0,0,0,1,2,4,6,8,12,16,20,26

%N Maximum number of edges a single edge crosses in a drawing of the complete graph K_n where every vertex lies on the outer face.

%e K_1, K_2, K_3 are all outerplanar graphs, and therefore have no crossings. K_4 can be drawn as a box with one crossing inside the box. K_5 can be drawn as a pentagram inside a pentagon, and in a drawing of a pentagram any edge crosses only two other edges.

%K nonn,more

%O 1,5

%A _Sam Barr_, Jul 13 2021