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This paper is concerned with structures of general graphs with perfectmatchings. We first reveal a partially ordered structure amongfactor-components of general graphs with perfect matchings. Our second resultis a generalization of Kotzig's canonical partition to a decomposition ofgeneral graphs with perfect matchings. It contains a short proof for thetheorem of the canonical partition. These results give decompositions which arecanonical, that is, unique to given graphs. We also show that there arecorrelations between these two and that these can be computed in polynomialtime.

A Partially Ordered Structure and a Generalization of the Canonical Partition for General Graphs with Perfect Matchings