Which assemblers don't rely on k-mers but can also be used for large genomes eg. vertebrates?
Could you maybe elaborate what kind of data you're using? E.g., if you're using Illumina short reads using a non deBruijn assembler doesn't make much sense. If you're using PacBio/Nanopore data, though, then have a look into Flye, Canu, or HGAP.
Masurca uses both, so might be interesting:
From the website https://github.com/alekseyzimin/masurca
"The MaSuRCA assembler combines the benefits of deBruijn graph and Overlap-Layout-Consensus assembly"
Celera Assembler (precursor to Canu) was overlap consensus to my knowledge.
More than a few OLC assemblers have been created, but many are not applicable to large genomes because of memory requirements (if you're talking short reads). Long reads are a different ballgame.