Why do different substances containing saturated hydrocarbons burns with different flame?
LPG is propane, butane or a mixture of both. Paraffin candle wax is $(CH_2)_n$

typically $C_{31}H_{64}$ (other, nonparaffin, waxes are also used in candles, like stearin, beeswax, etc.)
However, LPG is a gas from the start and can mix with air (i.e., oxygen) before it begins to burn, while candle wax has to be heated by the flame before it can begin to burn, so the outer periphery of candle wax vapor (the part of the vaporized candle not yet heated up to ignition) is very small - a dark zone surrounding the wick. The possibility of contact with oxygen is limited to this area.
You will notice a blue zone around the wick also - perhaps obscuring the dark zone closer to the wick. This is a hydrogen-rich flame; under ideal conditions, you can burn off all the hydrogen and leave the carbon (put a glass into the flame: it will get coated with black soot). But if you don't cool the flame with a glass, the carbon which would otherwise deposit will burn yellow.
So, &quot;insufficient supply of oxygen&quot; is an OK answer, but maybe a better one is &quot;scanty mixing of candle wax vapor with oxygen&quot;. I suspect that if you boiled candle wax rapidly in a closed container with a vent, and ignited the gases coming out of the vent, they would burn much more like LPG and less yellow.
The colors are dependent not only on line spectra of the atoms, but also on black body radiation from solid carbon. In the candle flame, by the time the carbon get access to oxygen, its temperature is not as high as in a LPG flame, and the possibility of solid carbon particles burning increases the amount of yellowish light emitted. Kind of like charcoal burning, but on a much smaller scale.