A search warrant for Kohberger's home, obtained by TMZ, says police seized several other notable items from the raid ... including items with dark red and brown stains.

The search warrant notes there was a significant amount of blood spilled in the murder house, with investigators saying they believe the killer would have blood evidence on their body or clothing.

Police were looking for trace evidence of blood stains in Kohberger's apartment, and the docs say there was a pillow with a "reddish/brown stain" and an item with a "collection of dark red" spotting.

The hair strand could be huge -- there was a dog in the students' home at the time of the murders, and the killer spared the pooch. According to the docs, cops went looking for hair at Kohberger's apartment, and found the possible animal hair ... as well as strands from humans.

The docs say a dog was heard barking at 4:17 AM the night of the murders ... the dog, Murphy, belonged to victim Kaylee Goncalves, and was found unharmed in her room.

Other items seized from Kohberger's place ... a computer tower, a disposable glove, mattress covers, receipts and a vacuum cleaner's dust container.

The docs say cops also searched Kohberger's office at Washington State University, where he was a graduate student studying criminology, but police didn't seize anything.

While cops say they found Kohberger's DNA on a knife sheath found inside the murder house ... the actual knife was not found in the search of Kohberger's home, or anywhere else for that matter.