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, 12, ... 個節點上的連通三次非哈密頓圖的數量為 2, 5, 35, 219, 1666, ... (OEIS A164919)。上圖顯示了一些非 snarks 的非哈密頓連通三次圖（snarks 被排除在外，因為 snarks 必然是非平面和非哈密頓的）。
>=38 都存在一個 
個節點的三次多面體非哈密頓圖 (Holton and McKay 1988, van Cleemput and Zamfirescu 2018)。
>=88 都存在這樣的圖 (van Cleemput and Zamfirescu 2018)。