d6.1. Year. If an event happens in the current year, it is not necessary to say June 6, 2003. It can stand as June 6. Anything that happened in a previous year would need the year. For example: Dec. 10, 2002.
d6.2. Use of "on" with dates. It is not necessary to use the word "on" when giving the date of an event. For example: Sam Smith died on Nov. 17. The sentence is clear without the "on." Sam Smith died Nov. 17. Same is true for wedding dates. Joe Jones and Carol Smith were married on Dec. 2, 2001. The "on" is not needed.