sentences:  In graph theory, a bipartite graph is a graph whose vertices are split into two colors, such that neighboring vertices have different colors.If a connected graph has no odd cycles, then a bipartition can be constructed by choosing a base vertex "v" and coloring every vertex black or white, depending on whether its distance from "v" is even or odd.Since the distance between "v" and itself is 0, and 0 is even, the base vertex is colored differently from its neighbors, which lie at a distance of 1.