For core strength I do alot of situps when I'm not working with equipment like bars and that kind of stuff. I do the pull ups. Taking a medicine ball and leaning back is another good one, but it doesn't build explosiveness, so I do it after cardio workouts, usually. It's also a nice stretch.
Heavybag lifts are my preferred core strength excercise, because it builds strength in the legs and in the core, essentially targetting all of the areas that are used in Roman Greco style takedowns.
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Barnett - Toquinho -Werdum - "Nurmie"
Z. Gurgel - Morango - Rocha - Tiequan