https://github.com/sleekpanther/bipartite-testing
Algorithm to test if a given graph is Bipartite or not
https://github.com/sleekpanther/bipartite-testing
algorithm bfs bipartite bipartite-graphs bipartite-test bipartite-testing breadth edges graph graph-algorithms graphs java noah noah-patullo pattullo patullo patulo
Last synced: 8 months ago
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Algorithm to test if a given graph is Bipartite or not
- Host: GitHub
- URL: https://github.com/sleekpanther/bipartite-testing
- Owner: SleekPanther
- Created: 2017-04-07T01:14:37.000Z (over 8 years ago)
- Default Branch: master
- Last Pushed: 2017-04-08T19:41:19.000Z (over 8 years ago)
- Last Synced: 2025-01-15T13:08:07.183Z (9 months ago)
- Topics: algorithm, bfs, bipartite, bipartite-graphs, bipartite-test, bipartite-testing, breadth, edges, graph, graph-algorithms, graphs, java, noah, noah-patullo, pattullo, patullo, patulo
- Language: Java
- Homepage:
- Size: 601 KB
- Stars: 0
- Watchers: 2
- Forks: 1
- Open Issues: 0
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Metadata Files:
- Readme: README.md
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README
# 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](https://github.com/SleekPanther/breadth-first-search-depth-first-search-graphs)
## 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