This is the 536th most frequent Polish word.
ukraińskich
"Ukraińskich" means "Ukrainian" (plural genitive or plural locative form) in English.
Here, 'ukraińskich' is used as an adjective, in plural form, describing the noun 'artystach' (artists), which is in the locative case.
Czytałem artykuły o ukraińskich artystach.
I read articles about Ukrainian artists.
In this sentence, 'ukraińskich' is an adjective, plural form, modifying 'podróżników' (travelers), which is in the accusative case.
Spotkaliśmy kilku ukraińskich podróżników.
We met several Ukrainian travelers.
'Ukraińskich' is used here as an adjective in plural, qualifying 'wsi' (villages), which is in the genitive case.