"core of competition" is a correct and usable phrase in written English.
You could use it in a sentence such as "The core of competition between the two companies was about pricing."
The better students seeking the better schools are the core of the competition, and in it, New York suburban students' academic strength is, paradoxically, their greatest disadvantage.
While he has taken college classes, Phelps missed out on the camaraderie and team-building at the core of collegiate competition.
In a statement the association also reiterated its support for Uefa, the European football governing body, and the current pyramid structure, in which promotion and relegation and the sporting merits of clubs are at the core of every competition.
At the core of successful competition is accomplishing goals within your peer group.
But if the US and China drift towards more open competition, the core of that rivalry will be who has better friends, and everyone in the region will have to make hard choices.
"The players that are available now, including the NRL-based players and the young players added to the core of senior lads, competition for places is as strong as I remember," Sinfield added.
Soul (or, as some prefer, the human spirit), on the other hand, is at the core of sportsmanship, cooperative competition and true success.
One of federalism's core virtues is the possibility of competition among states.
That fact gets lost in the common indictment of state and local immigration measures as a "patchwork". One of federalism's core virtues is the possibility of competition among states.
The core of his work is competition among so-called violence-managing agencies criminal groups, private security services, private protection companies, and informal protective agencies associated with the state which multiplied with the liberal reforms of the early 1990s.
