We present a logspace algorithm for computing a canonical labeling, in fact a canonical interval representation, for interval graphs. To achieve this, we compute canonical interval representations of interval hypergraphs. This approach also yields a canonical labeling of convex graphs. As a consequence, the isomorphism and automorphism problems for these graph classes are solvable in logspace.

For proper interval graphs we also design a logspace algorithm computing their canonical representations by proper and by unit interval systems.

The main result is now stated in the interval hypergraph setting, yielding also canonization of convex graphs. The hardness results are extended to interval hypergraphs and convex graphs as well. Finally, we also show how to compute proper and unit interval representations in logspace.

We present a logspace algorithm for computing a canonical interval representation and a canonical labeling of interval graphs. As a consequence, the isomorphism and automorphism problems for interval graphs are solvable in logspace.