This is the 16582nd most frequent Polish word.
wojewódzkich
"Of provincial" or "related to a voivodeship."
Here, 'wojewódzkich' acts as an adjective derived from 'województwo' (province), describing 'zawody sportowe' (sports competition) to mean provincial-level competitions.
Spotkałem go na wojewódzkich zawodach sportowych.
I met him at the provincial sports competition.
In this context, 'wojewódzkich' modifies 'centrach kultury' (cultural centers), indicating their association with a certain province.
Debaty odbywają się w wojewódzkich centrach kultury.
The debates take place in provincial cultural centers.
'Wojewódzkich' here is used to describe 'wyborów' (elections), meaning they pertain to the administrative region of a province.