Genome assembly with variable order de Bruijn graphs

Choosing an order for constructing a de Bruijn graph (DBG) is a crucial step in de novo assembly, as no single value allows complete genome reconstruction. The variable-order de Bruijn graph (voDBG) addresses this limitation by combining DBGs of multiple orders in a single structure connected by contextual relationships. This representation enables new connections to be identified or ambiguities to be resolved during assembly. However, voDBGs currently lack a formal definition of contigs. In this paper, we give the first formal definition of contigs for voDBGs. We show that, for a frequency range [{ell}, h] with{ell} > h/2, nodes whose labels occur with frequency f [isin] [{ell}, h] in the reads spell sequences of the genome with high probability under uniform sampling assumptions. We call these sequences ({ell}, h)-tigs. We also present an efficient algorithm to enumerate ({ell}, h)-tigs from a voDBG that accounts for homopolymer errors. Experiments on PacBio HiFi data show that our method significantly improves contiguity compared to fixed-order DBGs while remaining considerably lighter than full genome assemblers.