Yeast Strain with squalene synthase / farnesyltransferase (ERG9) gene deleted
Yeast strains have two mating types MATa (since it secretes a pheromone named 'a factor'), MATα (secretes pheromone 'α factor'). Both MATa and MATα strains are haploid and when they fuse together they form diploid zygote. A haploid yeast has only one set of genes and utilize chemicals like histidine and tryptophan (amino acids) and adenine (part of DNA, ATP and other molecules) for growing. Yeast strains mutant with any of genes to
make these chemicals they will not grow unless they can get these chemicals from their food (yeast media) or allowed to mate with strain having normal genes. 

Interpreting the strain notation:

BY4743; MATa/MATα; ura3Δ0/ura3Δ0; leu2Δ0/leu2Δ0; his3Δ1/his3Δ1; Met15Δ0/MET15; LYS2/lys2Δ0; YKL019w/YKL019w::kanMX4

Strain name: BY4743
Genotype: MATa/MATα; ura3Δ0/ura3Δ0; leu2Δ0/leu2Δ0; his3Δ1/his3Δ1; Met15Δ0/MET15; LYS2/lys2Δ0; YKL019w/YKL019w::kanMX4

To understand clearly, you can dissect the genotype in individual strains

BY4743;MATa;ura3Δ0;leu2Δ0;his3Δ1;met15Δ0;LYS2;YKL019w/YKL019w

BY4743;MATα;ura3Δ0;leu2Δ0;his3Δ1;MET15;lys2Δ0;kanMX4

Yeast genetics nomenclature:


Normal or wildtype genes are written in capitalized form - MET15 in MATα
Mutated genes are symbolized with small letter and Δ - ura3Δ0
ura3Δ0/ura3Δ0 - allelic mutation:  mutation in same genes of both strains (MATa/MATα) - They are two mutant alleles in the same gene locus. Both alleles of same gene are knocked out, so even both strains mate, they need external source of uracil in media to grow. Defect in one strain is NOT complemented by the other.
Met15Δ0/MET15 &amp; LYS2/lys2Δ0 - Non-allelic mutation: Defect in one strain is complemented by the other. MATa has Met15Δ0 (mutation in methionine gene) and MATα has wildtype MET15 gene, capable of met synthesis. Complementation works here.
YKL019w/YKL019w::kanMX4 - Critical aspect of yeast strain in functional complementation assays. In all commercially available yeast strains, one gene will be double knocked out (both alleles of same gene) and replaced with an auxotrophic markers like antibiotics - tetracycline, kanamycin, ampicillin - for selecting the diploid cells after mating two strains. It is similar to plating Kanamycin mixed LB media to pick E.coli colonies harboring Kanamycin resistance vector in it. 


The gene that is replaced is the gene of interest, i.e. if I am looking to study role of putative PGPS in Plasmodium falciparum, I get yeast strain knocked out with yeast PGPS (pgsΔ). When I do complementation test, I provide external DNA template cloned with Plasmodium falciparum's PGPS to check whether it complements in yeast genome and yeast grows - gene essentiality study.

I am not sure of the gene YKL019w/YKL019w, but it implies that wildtype of YKL019 is replaced with Kanamycin - kanMX4.