  Graph states (or cluster states) are the entanglement resource that enables
one-way quantum computing. They can be grown by projective measurements on the
component qubits. Such measurements typically carry a significant failure
probability. Moreover, they may generate imperfect entanglement. Here we
describe strategies to adapt growth operations in order to cancel incurred
errors. Nascent states that initially deviate from the ideal graph states
evolve toward the desired high fidelity resource without impractical overheads.
Our analysis extends the diagrammatic language of graph states to include
characteristics such as tilted vertices, weighted edges, and partial fusion,
which arise from experimental imperfections. The strategies we present are
relevant to parity projection schemes such as optical `path erasure' with
distributed matter qubits.
