The four are accused of killing Amos Beede at the camp in Burlington, the police chief, Brandon del Pozo, said at a news conference. Mr. Beede was beaten up on May 22 and suffered blunt force trauma to his brain, the police said. He died seven days later.
Law enforcement officials said they were not ruling out the possibility that the “brute force” assault on Mr. Beede had been a bias attack.
The suspects — two men and two women — were arrested Thursday night at Dog Beach in San Diego, a gathering place for the homeless. The police in at least three states joined forces to find them, partly with the help of technology that reads license plates and that tracks phones, officials said.
They fled Vermont after the attack and ended up in Roswell, N.M., where one of them had relatives, the police said. There, one suspect, Erik Averill, 21, was briefly taken into police custody after being accused of assaulting his partner, Myia Barber, 22, who is also a suspect in the fatal beating. But Mr. Averill was released, and the four continued their journey to California.
The police identified the other two suspects as Allison Gee, 25, and Jordan Paul, 21.
The four are being held in California on warrants accusing them of second-degree murder, Chief del Pozo said. It was not immediately clear when they would be sent to Vermont to face the charges.
The chief said the beating started over a dispute in the homeless camp; someone smeared feces on a tent from the south side of the encampment, and Mr. Beede was believed to have reacted by dumping urine in a north-side tent, the chief said.
Mr. Beede, 38, was not homeless. He had an apartment in Milton, but he was staying with friends at the encampment over the weekend because the local bus was not running, the police said.
Mr. Averill allegedly enlisted the help of the others to attack Mr. Beede, the chief said. Then the four fled in a Chevy Malibu. Officers in New Mexico helped track the suspects’ car, the police said.“There probably was not an elaborate escape plan,” Chief del Pozo said.
There were many witnesses to the beating, but further details were not available. The arrest warrant is sealed, the police said.
The mayor of Burlington, Miro Weinberger, said that the city had a chronic homelessness problem despite initiatives to remove the encampments in a “humane” way. The tents are in an industrial area known as the Pine Street Barge Canal.
“They really are full of squalor,” Chief del Pozo said.
In an interview with WPTZ, a Vermont television station, Mr. Beede’s sister said that he previously tried to advocate for toiletry supplies for the homeless residents at the camp, collecting donations of supplies through Facebook postings.
“And that is what Amos was about, was helping others,” said his sister, Ina McKinney.
Sitting next to their mother, Ms. McKinney said her family knew that Mr. Beede was “not going to make it” as soon as they saw him after the attack.
“He had motions in his arms, and it seemed like the same motion as if he was reaching for us to let us know that he knew we were there,” she said.