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The tripartite-circle crossing number of graphs with two small partition classes

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arxiv 2108.01032 v2 pith:ULRH26B4 submitted 2021-08-02 math.CO cs.DM

classification math.COcs.DM
keywords tripartite-circlenumbercrossingcirclesdrawinggraphpartitiontripartite
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

A tripartite-circle drawing of a tripartite graph is a drawing in the plane, where each part of a vertex partition is placed on one of three disjoint circles, and the edges do not cross the circles. The tripartite-circle crossing number of a tripartite graph is the minimum number of edge crossings among all its tripartite-circle drawings. We determine the exact value of the tripartite-circle crossing number of $K_{a,b,n}$, where $a,b\leq 2$.

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