What conditions must exist for a fire to occur?

In strictly theoretical terms, there must be fuel at a combustion temperature, with enough oxygen to support a flame, and a source of ignition to start the chemical reaction we know as "fire."

For example, paper can be ignited at 451 degrees Fahrenheit but will not ignite when heated to that temperature unless there is enough oxygen.

Gasoline, on the other hand, has a flash point of minus 40 degrees, meaning its fumes can be ignited at any temperature higher than that, but only if in the proper concentration (between the lower and upper flammable limits). In other Words, there has to be enough oxygen in the mixture to allow the gasoline fumes to burn.