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# Embedding complete bipartite graphs

• Prove that for every surface $S$ there exists an integer $t$ such that $K_{3,t}$ does not embed in $S$.

• What is the minimum value of $t$ such that $K_{3,t}$ does not embed in torus (a.k.a donut).

• What is the minimum value of $t$ such that $K_{t,t}$ does not embed in torus (a.k.a donut).

• What is the minimum value of $t$ such that $K_{t,t}$ does not embed on the surface formed by adding two handles to the sphere.

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Shiva Kintali
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Posted: Jun 10 '12

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Last updated: May 19