Authorities in Wisconsin believe they have solved Green Bay's oldest cold case with the arrest of a 65-year-old man they allege strangled Lisa Holstead to death back in 1986.

The arrest of Lou Griffin was announced Thursday. He was arrested at his house in Racine on a first-degree intentional homicide charge early the previous morning.

Holstead, 22, was killed with a piece of her own clothing back in August of 1986.

Her body was recovered from a marshy area of Green Bay near the Ken Euers Nature Park.

"He wasn't on anybody's radar back in 1986 when this homicide occurred," Green Bay Police Chief Andrew Smith told reporters in announcing the arrest.

Holstead was a single mother with one child. Police said she was last seen in Green Bay running from her boyfriend's car following an argument.

The couple lived together, and her boyfriend told investigators she never made it home that night.

According to court records obtained by PEOPLE, DNA from semen recovered from Holstead's body was compared with a DNA sample taken from the boyfriend in 1998. It was also entered into the national DNA database, but no match was returned.

Over the years, detectives started looking at Griffin as a possible suspect, noting he was released from prison on May 20, 1986, after being convicted in 1981 of second-degree child sexual assault.

When Holstead was murdered, Griffin apparently resided in Green Bay.

Smith did not discuss what led detectives to surveil Griffin in recent months, but they did.

In mid-September, police observed him smoking outside his residence, and retrieved the discarded filter. They also pulled beer cans from a dumpster outside his home.

Police alleged that Griffin sexually assaulted Holstead before killing her. Griffin denied knowing Holstead at first, and when confronted with the DNA evidence, allegedly acknowledged he may have slept with her but did not murder her.

"It's a good day that we believe we've solved a homicide," Smith told the press. "But it's also a sad day. Lisa Holstead lost her life. Her child lost his mother."

Griffin is being held on $1 million.

He will be asked to enter a plea to the charge against him during a hearing set for Dec. 10. It was unclear who his lawyer was Friday.