  Motivated by recent proposals of possible wormhole shape functions, we
construct a wormhole shape function by employing the Karmarkar condition for
static traversable wormhole geometry. The proposed shape function generates
wormhole geometry that connects two asymptotically flat regions of spacetime
and satisfies the required conditions. Further, we discuss the embedding
diagram in three-dimensional Euclidean space to present the wormhole
configurations. The main feature of current study is to consider three
well-known $f(R)$ gravity models, namely exponential gravity model, Starobinsky
gravity Model and Tsujikawa $f(R)$ gravity model. Moreover, we investigate that
our proposed shape function provides the wormhole solutions with less (or may
be negligible) amount of exotic matter corresponding to the appropriate choice
of $f(R)$ gravity models and suitable values of free parameters. Interestingly,
the solutions obtained for this shape function generate stable static
spherically symmetric wormhole structure in the context of non-existence
theorem in $f(R)$ gravity. This may lead to a better analytical representation
of wormhole solutions in other modified gravities for the suggested shape
function.
