When performing genetic knockouts in yeast using homologous recombination to replace a target gene sequence via a vector DNA, does the region between the flanking regions in the vector have to be the same length as the site of recombination in the host cell's gene?
As pointed out by aandreev, the greater the size of the insert relative to the flanks lower will be the recombination rate. This is because the donor DNA essentially becomes non-homologous. See the figures below:
Figure1: Effect of insert size on recombination efficiency. Kung et al. (2013) Appl Environ Microbiol. Mar;79(5):1712-7
Figure2: Effect of flank size on recombination efficiency. Kung et al. (2013) Appl Environ Microbiol. Mar;79(5):1712-7
However, you mentioned that you want to make gene knockouts. In this case you just need to make a small mutation (for example introducing a premature stop codon).
Use of genome editing tools such as Crispr-Cas, ZFN and TALEN increase the rate of transgenesis by introducing DNA double strand break.
These can also be used for making knockouts when NHEJ dominates over HR as the DNA repair mechanism. NHEJ is error-prone and can cause indels that can disrupt gene function.
In my view there is direct link between probability of recombination and size of the insert. Smaller inserts with larger flanks get incorporated easier. That I understand from reviewing studies based on Cas9/CRISPRs system. Same should stand for HR-mutagenesis in yeast.
So, short answer will be: shorter inserts are more efficient. However, I couldn't find any studies of relation between recombination efficiency and using smaller than target inserts, or relation between sizes of target and insert. Cas9/CRISPR system was used to insert loxP site (34nt) instead of ~10 bp in mice ES cells. People usually try to insert GFP or something similar in size instead of shorter genomic sequences.