If something's glutted, it's overfull or oversaturated. A glutted animal shelter has more cats and dogs than it has room for.

If your school bake sale is glutted with chocolate chip cookies, there are more than can possibly sell, and if a job market is glutted with elementary school teachers, there won't be enough positions available for all of them. The adjective glutted comes from glut, "an excessive supply," which originally meant "to feed to repletion," or to feed too much, from the Latin glutire, "to gulp down."

Definitions of glutted

adj exceeding demand

“a glutted market”
containing as much or as many as is possible or normal

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