The Hollow Man (1935 novel)

The Hollow Man is a famous locked room mystery novel by the American writer John Dickson Carr (1906-1977), published in 1935. It was published in the USA under the title The Three Coffins, and in 1981 was selected as the best locked-room mystery of all time by a panel of 17 mystery authors and reviewers

Plot summary
One wintry night in London, two murders are committed in quick succession. In both cases, the murderer has seemingly vanished into thin air.
In the first case, he has disappeared from Professor Grimaud's study after shooting the professor -- without leaving a trace, with the only door to the room locked from the inside, and with people present in the hall outside the room. Both the ground below the window and the roof above it are covered with unbroken snow.
In the second case, a man walking in the middle of a deserted cul-de-sac at about the same time is evidently shot at close range, with the same revolver that killed Grimaud and only minutes afterward, but there is no one else near the man; this is witnessed from some distance by three passersby -- two tourists and a police constable -- who happen to be walking on the pavement. It takes Dr Gideon Fell, scholar and "a pompous pain in the neck," who keeps hinting at the solution without giving it away,

Perfect murder (fiction)

The perfect murder is a murder which benefits the murderer, but also has no negative consequences for him or her; usually, this simply means that the murderer is never caught. Several factors might contribute to the perfect murder:
The murderer has an impeccably trustworthy witness who provides an alibi, which no other witness contradicts.
The murderer had no apparent motive to commit the crime, and thus is not suspected by investigators.
The murderer does not retain incriminating items or leave physical evidence of his presence at the crime scene.
The murderer cannot be convicted for the crime owing to a legal loophole that the murder knew would make a conviction unattainable.
At no stage in planning, committing or covering up the crime does the murderer take another person into confidence on any suspicious or illegal matter.

The concept of the perfect murder is closely connected with detective fiction and often crops up in the whodunit and the locked room mystery. In the latter case, the murderer usually tries to make their crime 'perfect' by creating the illusion that there is no physically possible way they could commit the crime. For example, the victim is found dead in an empty room with its only door locked from the inside. The murderer, of course, has used some clever method to lock the door after departure, and a verdict of suicide means that foul play is not suspected.
The idea of a "motiveless" perfect murder is explored in the novel Strangers on a Train by Patricia Highsmith, famously adapted into a movie by Alfred Hitchcock. The scheme is for two strangers who both want someone dead to meet randomly and "trade murders," each doing the other's dirty work so they each have no discernible motive for their respective crimes.
A perfect murder could involve making it appear that the person one kills is oneself. The film The Whole Nine Yards features a perfect murder in which a hitman kills someone and blows up his body, making facial identification impossible. Knowing the police would check the body's dental records, the killer has a dentist insert dental implants to modify the victim's teeth to match his own.
A perfect murder could also be made to appear as an accidental or natural death.