README.md

List of graph-related topics in competitive programming, organized from basic to advanced:

Basic Graph Concepts:

1. Graph Representation
   • Adjacency Matrix
   • Adjacency List
2. Graph Traversal
   • Depth-First Search (DFS)
   • Breadth-First Search (BFS)

Intermediate Graph Algorithms:

3. Shortest Path Algorithms
   • Dijkstra's Algorithm
   • Bellman-Ford Algorithm
4. Minimum Spanning Tree (MST)
   • Kruskal's Algorithm
   • Prim's Algorithm
5. Union-Find / Disjoint Set Union (DSU)
   • Path Compression
   • Union by Rank/Size
6. Topological Sorting
7. Strongly Connected Components (SCC)
   • Kosaraju's Algorithm
   • Tarjan's Algorithm
8. Cycle Detection
   • In Directed Graphs
   • In Undirected Graphs

Advanced Graph Algorithms:

9. Flow Algorithms
   • Ford-Fulkerson Method
   • Edmonds-Karp Algorithm
   • Dinic's Algorithm
10. Matching Algorithms
    • Bipartite Matching
    • Hopcroft-Karp Algorithm
11. Eulerian Path and Circuit
    • Hierholzer's Algorithm
12. Hamiltonian Path and Circuit
    • Backtracking
    • Dynamic Programming Approach
13. Network Flow
    • Min-Cost Max-Flow
14. Graph Coloring
    • Greedy Coloring
    • Backtracking
    • Bipartite Check
15. Planarity Testing
16. LCA (Lowest Common Ancestor)
    • Binary Lifting
    • Euler Tour Technique
17. Tree Algorithms
    • Tree Diameter
    • Centroid Decomposition
    • Heavy-Light Decomposition
18. 2-SAT Problem
19. Articulation Points and Bridges
20. Graph Isomorphism

Specialized Topics:

21. Suffix Tree and Suffix Array
22. Persistent Data Structures in Graphs
23. Dynamic Graph Algorithms
    • Dynamic Connectivity
    • Dynamic MST
24. Expander Graphs
25. Graph Compression Techniques
    • Heavy Path Decomposition
    • Tree Decomposition