Pyrotechnic "star" without oxidizer
When the interior gunpowder charge explodes, it blows the stars in all directions and ignites them.  They then burn very rapidly (perhaps explosively) giving the star effect exactly because the stars are a mixture of fuel and oxidizer.  If the stars were all fuel (carbon), they would be essentially charcoal briquettes.  In that case the center would explode, throwing (possibly) burning charcoal chunks in all directions.  This could be a truly novel approach to barbecue...