  An interesting class of scalar-tensor models, denoted by kinetic gravity
braiding (KGB), has recently been proposed. These models contain interactions
of the second derivatives of the scalar field that do not lead to additional
degrees of freedom and exhibit peculiar features, such as an essential mixing
of the scalar $\phi$ and tensor kinetic $X$ terms. In this work, we consider
the possibility that wormhole geometries are sustained by the KGB theory. More
specifically, we present the full gravitational field equations in a static and
spherically symmetric traversable wormhole background, and outline the general
constraints at the wormhole throat, imposed by the flaring-out conditions.
Furthermore, we present a plethora of analytical and numerical wormhole
solutions by considering particular choices of the KGB factors. The analysis
explicitly demonstrates that the KGB theory exhibits a rich structure of
wormhole geometries, ranging from asymptotically flat solutions to
asymptotically anti-de Sitter spacetimes.
