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In this article, we study the existence of a 2‐factor in a K1, n‐free graph. Sumner [J London Math Soc 13 (1976), 351–359] proved that for n⩾4, an (n−1)‐connected K1, n‐free graph of even order has a 1‐factor. On the other hand, for every pair of integers m and n with m⩾n⩾4, there exist infinitely many (n−2)‐connected K1, n‐free graphs of even order and minimum degree at least m which have no 1‐factor...
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