Claims

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1961_01_01_posa: Pósa proves that every graph on n at least 4 vertices with at least 2n-3 edges has a cycle with a chord, so g_1(n) = 2n-4 for n at least 4, the case k = 1 of Problem 767; posed as Problem 127 of Mat. Lapok 12 (1961).

2004_04_07_jiang: Jiang proves that the most edges on n vertices with no cycle carrying k chords at one cycle vertex is (k+1)n minus (k+1) squared for all n at least 3k+3; a refereed note in J. Graph Theory 46 (2004), known by its abstract.

2026_09_14_chen_ning: Chen and Ning prove an exact formula for the most edges on n vertices with no cycle carrying k chords at one cycle vertex, for every k and n at least k+2, with a sharp threshold near 5k/2; a 2026 preprint with its own Lean.

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