  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 $k\leq 2$ was proved by Bondy and Vince, which resolved an earlier
conjecture of Erd\H{o}s et. al.. In this paper we confirm this conjecture for
all $k$.
