نظریه گراف‌ها برای المپیاد کامپیوتر
  • Basic definitions
    • Introduction and Modeling with Graphs
    • Types of Graphs
    • Graph Implementation
    • Walk, Trail, Path, Extremal
    • Subgraphs
    • Connectivity, Cut Edge, and Cut Vertex
    • Bipartite Graph
  • Trees
    • Basic Properties
    • Distance in Trees and Graphs
    • Counting the Number of Trees
    • DFS
    • BFS
    • گراف و نمایش ماتریسی آن
    • Directed Graphs
    • Undirected Graphs
    • Adjacency Matrix
    • Adjacency List
    • Edge List
    • Graph Representation
    • نمایش گراف
    • Depth-First Search (DFS)
    • الگوریتم جستجوی اول عمق (DFS)
    • Directed Graphs
    • الگوریتم جستجوی عمق اول (DFS)
    • Bipartite Graphs
    • Spanning Trees
    • Trees
    • الگوریتم جستجوی اول سطح (BFS)
    • ماتریس مجاورت
    • لیست مجاورت
    • لیست یالها
    • الگوریتم جستجوی اول سطح
    • BFS و DFS در یک گراف
    • تعاریف گراف
    • Representing a Graph Using an Edge List
    • گراف‌های جهت‌دار
    • Introduction
    • Graph Representation
    • Graph Traversal
    • Important Algorithms
    • Algorithm for Finding the Diameter of a Tree
    • Checking Ancestor-Descendant Relationship in Linear Time
    • Finding the k-th Ancestor
    • Bi-connecting with Minimum Number of Paths
    • Vertex and Edge Cut Algorithms
    • Idea Cultivation Workshop
  • Directed graph
    • Definitions
    • Tournament
    • Directed Acyclic Graph (DAG)
    • Strongly Connected Components
    • Detecting Cycles in Directed Graphs
    • Games and Directed Graphs
    • Functional Graphs and Permutation Graphs
  • Proof technics in graph problems
    • Extremal Choices
    • Contraction
    • Graphs and Magic
  • Euler circuit and hamiltonian cycle
    • Introduction
    • Eulerian Tour in Directed and Undirected Graphs
    • De Bruijn sequence
    • Existence Theorems for Hamiltonian Cycles
    • Exponential Algorithms for Finding Hamiltonian Cycles and Paths
    • مسئله فروشنده دورهگرد (الگوریتم پویا)
  • Shortest path algorithms
    • Bellman-Ford
    • Dijkstra
    • Floyd-Warshall
  • Matrix
    • Matrices and Operations on Them
    • Kirchhoff's Theorem
    • Incidence Matrix
    • Adjacency Matrix
    • Number of Walks of Length n
    • Deriving Recursive Functions Using Graphs and Matrices
  • Tree data structures
    • Binary Tree
    • Binary Search Tree (BST)
    • Heap
    • DSU
    • Segment Tree
    • Search (Search)
    • Insertion (Insertion)
    • Applications
  • NP and NP-complete problems
    • Definition of NP and NP-Completeness
    • Problem Definitions
    • Reducing the circuit-sat Problem to sat
    • NP-Complete Graph Problems
  • LCA
    • Problem Statement
    • An O(n + q*lg(n)) Solution Using Heavy-Light Decomposition
    • Tarjan's Offline Algorithm
    • The Relationship Between LCA and RMQ
    • A Linear Approach to LCA
    • Virtual Tree
  • Advanced tree algorithms
    • Minimum Spanning Tree
    • Guni
    • Centroid
    • Huffman Coding
    • Tree Hash
    • Heavy-Light Decomposition (HLD)
  • Connectivity
    • Cuts and Connectivity
    • k-Connected Graph
    • Minimum Cut and Maximum Flow
  • Matching
    • Introduction
    • Matchings in Bipartite Graphs
    • Minimax Theorems
    • Applications
    • Maximum Flow and Matching
    • Poset
    • Matchings in General Graphs
  • Extra topics
    • Drawing a Planar Graph on a Sphere
    • Euler's Theorem
    • Dual Graph
    • Degree Sequence
    • Coloring
    • Isomorphism
    • Random Walk
    • Ramsey Numbers
    • Independent Set and Clique
    • مکمل گراف
    • 2-SAT
    • Some Special Matrices
  • Appendix
    • چگونه از این کتاب استفاده کنیم؟
    • آشنایی با الگوریتم ها و پیچیدگی
    • برگه تقلب (Cheat sheet)
  Index      جستجو

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Last updated at آوریل 19, 2025.

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