  Let $G$ be a graph, $C$ a longest cycle in $G$ and $\overline{p}$,
$\overline{c}$ the lengths of a longest path and a longest cycle in
$G\backslash C$, respectively. Almost all lower bounds for the circumference
base on a standard procedure: choose an initial cycle $C_0$ in $G$ and try to
enlarge it via structures of $G\backslash C_0$ and connections between $C_0$
and $G\backslash C_0$ closely related to $\overline{p}$, $\overline{c}$ and
connectivity $\kappa$. Actually, each lower bound obtained in result of this
procedure, somehow or is related to $\kappa$, $\overline{p}$, $\overline{c}$
but in forms of various particular values of $\kappa$, $\overline{p}$,
$\overline{c}$ and the major problem is to involve these invariants into such
bounds as parameters. In this paper we present a lower bound for the
circumference involving $\delta$, $\kappa$ and $\overline{c}$ and increasing
with $\delta$, $\kappa$ and $\overline{c}$.
