Does a Bipartite Graph Always Have a Chromatic Number of 2?

Indeed, a bipartite graph consistently boasts a chromatic number of two.

In a bipartite graph, the set of vertices divides neatly into two distinct clusters, allowing every edge to bridge a vertex from one cluster to another without any edges connecting vertices within the same cluster. This characteristic is the backbone of the bipartite concept, illustrated by our guide on bipartite graphs.

Here's a visual example of a bipartite graph.

In this scenario, the chromatic number—the least amount of colors needed to paint the vertices such that adjacent vertices do not share a color—assertively stands at 2. This principle is rooted in the bipartite graph's structure, ensuring a straightforward coloring approach.

Due to the clear separation of vertex groups, with zero edges linking vertices within the same group, we can apply one color to all vertices in one group and a contrasting color to the other group's vertices. This strategy guarantees that any two connected vertices will exhibit differing colors, elegantly satisfying the conditions for graph coloring and