The California State University campus at Long Beach graduated 8,720 students last month. Each one got the opportunity to walk the stage, and F. King Alexander, the university's president, shook every hand. California State at Long Beach has made graduating a greater number of its 38,000 students its top priority. The slogan "Graduation Begins Today" is everywhere on this campus, from banners to napkins in dining halls. The real novelty, however, is that Mr. Alexander says the university's graduation rate is less important than the sheer number of students who graduate. Long Beach graduates 54 percent of its students in six years, up from 35 percent in 2001. While experts call the current rate respectable for a regional public institution, Mr. Alexander says he could easily improve it to 90 percent by cherry-picking the most qualified students from the 65,000 applications the university receives each year and accepting fewer nontraditional and local students. But becoming more exclusive would not help California, argues Mr. Alexander, who often says Long Beach contributes more to its region than an Ivy League institution would. The state university produces teachers, engineers, and nurses who stick around to work in the city of Long Beach, which, like the campus, has one of the nation's most ethnically diverse populations. The university must also serve local students, 90,000 of whom attend schools within eight miles of the campus. Charles B. Reed, chancellor of the California State system, praises Long Beach for its success in helping more students graduate. But he would also like to see the university's graduation rate top 70 percent. But both Cal State and Long Beach officials say they must continue to accept lower and middle-income students, who are more likely to need extra help to graduate. "It's our responsibility as part of the public schools to get them ready," says Mr. Alexander. "We can't just turn them away."