Twenty years ago Bondy and Vince conjectured that for any nonnegative integer k, except finitely many counterexamples, every graph with k vertices of degree less than three contains two cycles whose lengths differ by one or two. The case $k\le 2$ was proved by Bondy and Vince, which resolved an earlier conjecture of Erdős et al. In this paper we confirm this conjecture for all k.

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关于邦迪和文斯的猜想

二十年前，邦迪（Bondy）和文斯（Vince）推测，对于任何非负整数k，除有限的许多反例外，每个k顶点的度数小于3的图都包含两个长度相差一或两个的循环。案子$ķ\le 2$Bondy和Vince证明了这一点，它解决了Erdős等人的早期猜想。在本文中，我们确认了所有k的猜想。