Even as a 14 -year-old, he managed to become Junior Champion of Yugoslavia, two years later he won the national championship by a split 4th - 7th Place in the Yugoslav Championship. In 1951, he won a 18- year-old the first Junior World Championship U20, which organized the FIDE. In the years 1964 - 1979 he qualified five times for the inter-zone tournament and came once, in Amsterdam, 1964 ( 7th place), the candidates tournament. He lost in the quarterfinals (Bled 1965) against the Dane Bent Larsen with 2,5:5,5 ( 1, -4, = 3).
Ivkov represented since 1956 Yugoslavia 12 times in chess Olympiads and was with his team six silver medals and three bronze medalists. As a single player, he won two gold medals for the highest individual score in each of his board at the Olympics.
His best tournament result achieved Ivkov 1965 in Zagreb, when he shared first place with Wolfgang Uhlmann and the reigning world champion Tigran Petrosian left behind. Ivkov won five league titles Yugoslavia. In 2006 he became European champion in the senior in Davos.
Due to his international success, he received in 1955 by FIDE the title of Grand Master.
His best historical Elo rating of 2715, he reached in October 1956 His current Elo rating is 2411 (as of April 2008)..