  An amino acid sequence of a protein may be decomposed into consecutive
overlapping strings of length K. How unique is the converse, i.e.,
reconstruction of amino acid sequences using the set of K-strings obtained in
the decomposition? This problem may be transformed into the problem of counting
the number of Eulerian loops in an Euler graph, though the well-known formula
must be modified. By exhaustive enumeration and by using the modified formula
we show that the reconstruction is unique at K equal or greater than 5 for an
overwhelming majority of the proteins in the PDB.seq database. The
corresponding Euler graphs provide a means to study the structure of repeated
segments in protein sequences.
