RICHMOND, Va. — Before Jesse Matthew killed 18-year-old University of Virginia student Hannah Graham, authorities say he left a trail of DNA evidence linking him to a 2005 rape and the 2009 slaying of another female student.

That link could have been uncovered when Matthew was convicted of trespassing in 2010, but authorities didn't take a DNA sample. Virginia law didn't call for it.

For Sue Graham, that's one of the most painful aspects of her daughter's slaying: knowing that her killer could have been locked up and unable to prey on her if only police had been able to take that DNA sample.

Graham and her husband, John, have been lobbying Virginia lawmakers to add trespassing and several other misdemeanors to the list of crimes that trigger mandatory DNA collection. It's part of a nationwide movement to expand DNA databanks by including misdemeanors ranging from shoplifting to trespassing to destruction of property.

Currently, 42 states and the District of Columbia collect DNA for certain sexual misdemeanor convictions. At least 26 states, including Virginia, collect DNA for a limited number of non-sexual misdemeanors. Three states — New York, Wisconsin and Utah — collect DNA for large numbers of misdemeanors.

Had police swabbed the inside of Matthew's cheek after his trespassing conviction, that DNA sample could have connected him to the 2009 slaying of 20-year-old Virginia Tech student Morgan Harrington. Her case remained a mystery for years, until Matthew was charged with killing Graham. Matthew pleaded guilty to the two slayings in 2016.

"He was flying under the radar. Had his DNA been tested in 2010, he would have been convicted of those offenses, and I have no doubt Hannah would be alive today," Sue Graham said. "It's a hard thing to have to acknowledge."

Proponents of increasing the number of crimes requiring DNA samples say it's simple logic: more samples mean more likely "hits" — matches of DNA left at crime scenes to samples in a databank — and more crimes solved or prevented.

But opponents say making DNA samples mandatory for crimes as minor as shoplifting or trespassing is going too far.

"We have the highest degree of sympathy for anyone who's lost a loved one through a violent crime, but subjecting hundreds of thousands of people to law enforcement scrutiny who haven't committed that kind of offense and never will is a problem," said Bill Farrar, a spokesman for the American Civil Liberties Union of Virginia.

In 1989, Virginia became the first state in the nation to require certain offenders to give DNA samples for a databank. The state has added offenses, and the number of samples in the databank had grown to about 441,500 by the end of June 2017.

Virginia law already requires DNA collection upon conviction for 14 misdemeanors, most related to sexual offenses. Two pending bills would add up to seven more, including: assault and battery; assault and battery against a family or household member; trespassing; concealing merchandise; destruction of property; obstruction of justice; and the theft of property valued at less than $200.

In New York, authorities began collecting DNA in 1996, initially only from people convicted of homicide and some sex offenses. In 2012, the state created an "all crimes" databank, requiring DNA samples from anyone convicted of all felonies and more than 200 misdemeanors.

DNA samples taken because of the expansion have produced nearly 1,800 investigative leads. Of those, 95 were linked to homicides, according to the New York Division of Criminal Justice Services. Spokeswoman Janine Kava said the agency does not track how many of those leads resulted in arrests or convictions.

Richard Aborn, president of the Citizens Crime Commission of New York City, said the expanded databank has benefited crime victims and defendants.

"DNA helps exonerate the innocent, holds offenders accountable, prevents future crimes, provides justice for survivors, and helps solve crimes — especially cold cases that have been unresolved for decades," Aborn said.

Since Virginia began adding misdemeanors to its databank in 2012, there had been 26 hits as a result of misdemeanor conviction samples, as of November 2017. The first hit in 2016 was linked to a sex offense case from 1997. Most of the hits have helped solve burglary and larceny convictions.

Del. David Toscano, chief sponsor of a bill that would add three new misdemeanors to Virginia's databank, said Hannah Graham's murder has been a driving factor.

"DNA has proven to be a very powerful tool to help people who might have been unjustly convicted. In the aftermath of the Hannah Graham case, you realize that the power of DNA can also help convict people who are guilty before they commit a subsequent offense," Toscano said.

But the ACLU says collecting DNA for minor crimes is an invasion of privacy.

"What is the right of the government to keep your personal information? ... It's unconstitutional," Ferrar said.

Sue Graham said she believes adding a handful of misdemeanors will be minimally intrusive and is a small inconvenience compared to the potential benefits.

"If things can be changed to help other young women in the future, then we believe that that should be done," she said.