If BT20-037 [Chaosmon: Valdur Arm] has this card, a yellow level 6 card, and a green level 6 card in its digivolution cards, then this card's inherited effect causes its DP to become 0 and it's deleted, does BT20-037 [Chaosmon: Valdur Arm]'s <Partition (Yellow Lv.6 + Green/Black Lv.6)> trigger?
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Yes, it triggers. When deletion occurs by DP becoming 0, it's considered deletion by the rules, therefore <Partition>'s trigger conditions are met.
Source: BT20-099 Singularity of Chaos