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 \(E(G)=E(G_1)\cup E(G_2)\).
The best solution was submitted by Huy Tùng Nguyễn (수리과학과 2016학번). Congratulations!
Here is his solution of problem 2018-14.