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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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updated May 19

kintali gravatar image Shiva Kintali flag of United States
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