Daily Archives: September 12, 2018

Status: 2018-14 Forests and Planes

At the moment, this problem remains open.

Suppose that the edges of a graph \(G\) can be colored by 3 colors so that there is no monochromatic cycle. Prove or disprove that \(G\) has two planar subgraphs \(G_1,G_2\) such that \(E(G)=E(G_1)\cup E(G_2)\).

Hint: The answer is NO. Disprove it.

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