Bipartite Graph Testing Algorithm

Modification of Breadth First Serach to check if a graph is bipartite
Uses the same BFS approach as I use in BFS/DFS Algorithms

Bipartite Graphs

A bipartite graph is one that can be partitioned into 2 sets of vertices where no edge has both end-nodes in the same set
A helpful abstraction is to imagine coloring the vertices 1 of 2 colors so that every edge has end-nodes of different colors

This is the 1st graph tested in the code

An important property of Bipartite graphs is they contain NO odd-length cycle
A Bipartite Graph (even length cycle)

A Non-Bipartite Graph (odd length cycle CANNOT be colored & still maintain edges with different colored end-nodes)

This is the 2nd graph that the code tests

Algorithm

• Modification of Breadth First Search
• Explore from any arbitrary node
• Color all nodes in a layer of BFS Red if if layer number is even, Blue if odd
• Scan edges to see if any edge with the same color on both ends (return false if that's the case)

Code Notes

• Uses an adjacency list graph representation
• String[] color is calculated during BFS based on if layerCounter is even or odd