A chemical process in which a substance reacts with oxygen to give off heat is called combustion. Heat and energy are produced in this reaction. 

When a chemical reaction occurs between a fuel and an oxidant, it leads to the formation of a combustion reaction. Combustion reactions always give the same products. 

The main one is energy, as combustion reactions are carried out to produce energy. The other products are carbon dioxide and water. 

During combustion, the carbon of the hydrocarbon combines with oxygen to form carbon dioxide. 

As in option C, carbon dioxide is not formed, hence it is not a combustion reaction.

Hence the correct answer is (C) $\mathrm{C}+\frac{1}{2}{\mathrm{O}}_2\to \mathrm{CO}$.