What do Eulerian and Hamiltonian cycles have to do with genome assembly?
Fig 1
A worked out example for a set of reads R = {TATTA, TAATA} and k = 3.
Here, the set of all k-mers is S = spk(R) = {TAT, ATT, TTA, TAA, AAT, ATA}. Panel A shows G1 = dBGk(S) and one possible Eulerian cycle of G1 (in blue). Panel B show the only other Eulerian cycle in G1 (in orange). The genome reconstruction corresponding to the blue cycle is ATTAATAT and to the orange cycle is ATTATAAT (note that because the genome is circular, the last 2 characters of each string are equal to the first 2 characters).