let's trace graph = [[1,3],[0,2],[1,3],[0,2]]. Start: color = [-1,-1,-1,-1]. Node is uncolored. BFS from : color as . Queue: [0]. Pop . Neighbors: , . Both uncolored. Color as , color as . Queue: [1, 3]. Pop . Neighbors: , . has color (opposite of , good). uncolored.
Color as . Queue: [3, 2]. Pop . Neighbors: , . Both already colored correctly. Pop . Neighbors: , . Both already colored correctly. No conflicts. Return true.