The two sentences that effectively combine the original sentences using a subordinating conjunction are:
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Although the International Astronomical Union determined that Pluto did not meet the criteria needed to be considered a planet, Pluto was downgraded to the status of a dwarf planet in 2006.
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After the International Astronomical Union determined that Pluto did not meet the criteria needed to be considered a planet, Pluto was downgraded to the status of a dwarf planet in 2006.
Both options use subordinating conjunctions ("although" and "after") to create a dependent clause that relates to the main clause.