Erdős Problem #1018 — Small nonplanar subgraphs in moderately dense graphs

About 55 years old · traced to

For every ε>0ε>0, is there a constant cεc_ε such that every nn-vertex graph with ⌊n1+ε⌋⌊n^{1+ε}⌋ edges contains a nonplanar subgraph on at most cεc_ε vertices?

References

Additional references

P. Erdős, Some unsolved problems in graph theory and combinatorial analysis, Combinatorial Mathematics and its Applications (Proc. Conf., Oxford, 1969), Academic Press (1971), 97–109.

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