Claims

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1996_03_01_komlos_szemeredi: Komlós and Szemerédi prove, by refining their earlier method, that a constant times r^2 n edges on n vertices force a subdivision of the complete graph on r vertices, an independent second proof answering Problem 718.

1996_09_01_bollobas_thomason: Bollobás and Thomason prove that every graph on n vertices with at least 256 r^2 n edges contains a subdivision of the complete graph on r vertices, which answers Problem 718 affirmatively with the constant 256.

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