Nouns

(n)dogfighta fiercely disputed contest“their rancor dated from a political dogfight between them”, “a real dogfight for third place”, “a prolonged dogfight over their rival bids for the contract”
(n)dogfightan aerial engagement between fighter planes
(n)dogfighta violent fight between dogs (sometimes organized illegally for entertainment and gambling)

Verbs

(v)dogfightarrange for an illegal dogfight
(v)dogfightengage in an aerial battle with another fighter plane