There are number of govt universities in Karnataka, as you want to do graduation from any one , so on you demand here I am providing list of them

Bangalore University
Bangalore

Visvesvaraya Technological University
Belgaum

National Law School of India University
Bangalore

Karnatak University
Dharwad

University of Mysore
Mysore

Kuvempu University
Shankaraghatta

Mangalore University
Mangalore

Tumkur University
Tumkur

Gulbarga University
Gulbarga

Davangere University
Davanagere

Kannada University
Hampi

Karnataka Veterinary, Animal and Fisheries Sciences University
Bidar

Karnataka State Law University
Hubli

Karnataka Folklore University, Haveri
Haveri

Karnataka State Music University, Mysore
Mysore

Rani Channamma University, Belgaum
Belgaum

Karnataka State Open University
Mysore

Karnataka State Women's University
Bijapur

Vijayanagara Sri Krishnadevaraya University
Bellary

University of Agricultural Sciences, Dharwad
Dharwad

University of Agricultural Sciences, Bangalore
Bangalore

Rajiv Gandhi University of Health Sciences
Bangalore

University of Agricultural Sciences, Raichur
Raichur

University of Horticultural Sciences, Bagalkot
Bagalkot

University of Agricultural and Horticultural Sciences, Shimoga
Shimoga