San Francisco police Tuesday arrested a homeless man for allegedly lighting another homeless man on fire earlier this month as the man lay sleeping in Golden Gate Park.

The suspect, 47-year-old Eric Dilbeck, was already in custody on another charge when police arrested him at the county jail Tuesday for the attempted murder of Bryon Rowe.

Rowe, 55, was asleep in the grass in Sharon Meadow at about 1 p.m. on Nov. 13 when police say Dilbeck poured lighter fluid on him and set him ablaze.

Rowe was rushed to the hospital with second- and third-degree burns on his back, police spokeswoman Lt. Lyn Tomioka said. He required skin grafts and remains at the hospital.

“The fortunate thing was that this victim had layers of clothing on, Tomioka said. “This could have been much worse if he didn’t have two coats on.”

The two men were believed to have known each other, but the motive for the attack is unknown, Tomioka said.

Tomioka credited “good police work” in identifying Dilbeck as the alleged attacker. She said several other people in the park witnessed the attack, but initially did not come forward to police.

Police later combed the park and found witnesses who said they knew Dilbeck and identified him as the suspect from a photo spread, according to Tomioka.

Dilbeck was recently arrested on Oct. 31 for public drunkenness and again on Nov. 18, for possessing marijuana for sale.

He was booked Tuesday on suspicion of attempted murder, arson resulting in injury and assault.

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