  An undirected graph $G$ is known to both the prover $P$ and the verifier $V$,
but only $P$ knows a subgraph $H$ of $G$. Without revealing any information
about $H$, $P$ wants to convince $V$ that $H$ is a connected spanning subgraph
of $G$, i.e. $H$ is connected and contains all vertices of $G$. In this paper,
we propose an unconventional zero-knowledge proof protocol using a physical
deck of cards, which enables $P$ to physically show that $H$ satisfies the
condition without revealing it. We also show applications of this protocol to
verify solutions of three well-known NP-complete problems: the Hamiltonian
cycle problem, the maximum leaf spanning tree problem, and a popular logic
puzzle called Bridges.
