05Cxx Graph theory
This subtopic studies graph theory, covering graphs, networks, colorings, embeddings, and the structural and algorithmic methods used to analyze them.
Specific topics
05C05 Trees
Overview
This specific topic studies trees within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for trees
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks
05C10 Planar graphs; geometric and topological aspects
Overview
This specific topic studies planar graphs; geometric and topological aspects within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for planar graphs; geometric and topological aspects
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks
05C12 Distance in graphs
Overview
This specific topic studies distance in graphs within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for distance in graphs
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks
05C15 Coloring of graphs and hypergraphs
Overview
This specific topic studies coloring of graphs and hypergraphs within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for coloring of graphs and hypergraphs
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks
05C20 Directed graphs (digraphs)
Overview
This specific topic studies directed graphs (digraphs) within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for directed graphs (digraphs)
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks
05C21 Flows in graphs
Overview
This specific topic studies flows in graphs within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for flows in graphs
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks
05C25 Graphs and abstract algebra
Overview
This specific topic studies graphs and abstract algebra within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for graphs and abstract algebra
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks
05C30 Enumeration in graph theory
Overview
This specific topic studies enumeration in graph theory within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for enumeration in graph theory
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks
05C35 Extremal problems in graph theory
Overview
This specific topic studies extremal problems in graph theory within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for extremal problems in graph theory
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks
05C38 Paths and cycles
Overview
This specific topic studies paths and cycles within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for paths and cycles
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks
05C40 Connectivity
Overview
This specific topic studies connectivity within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for connectivity
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks
05C45 Eulerian and Hamiltonian graphs
Overview
This specific topic studies eulerian and hamiltonian graphs within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for eulerian and hamiltonian graphs
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks
05C50 Graphs and linear algebra (matrices, eigenvalues)
Overview
This specific topic studies graphs and linear algebra (matrices, eigenvalues) within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for graphs and linear algebra (matrices, eigenvalues)
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks
05C55 Generalized Ramsey theory
Overview
This specific topic studies generalized ramsey theory within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for generalized ramsey theory
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks
05C63 Infinite graphs
Overview
This specific topic studies infinite graphs within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for infinite graphs
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks
05C69 Domination in graphs
Overview
This specific topic studies domination in graphs within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for domination in graphs
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks
05C80 Random graphs
Overview
This specific topic studies random graphs within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for random graphs
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks
05C81 Random walks on graphs
Overview
This specific topic studies random walks on graphs within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for random walks on graphs
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks
05C85 Graph algorithms
Overview
This specific topic studies graph algorithms within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for graph algorithms
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks
05C90 Applications of graph theory
Overview
This specific topic studies applications of graph theory within graph theory. It focuses on core definitions, canonical constructions, and key results used to analyze structures and prove classification or existence statements in graph theory.
Related Wikipedia Page
Graph theory (Wikipedia)
Useful Links
Key Ideas
- Formal definitions and equivalent formulations for applications of graph theory
- Representative theorems, extremal bounds, or invariants
- Connections to adjacent methods in graph theory
Typical Uses
Used to structure proofs, compare examples and counterexamples, and select appropriate tools when working on problems in graph theory.
Applications
- Theoretical research and classification questions
- Algorithmic or computational formulations where relevant
- Cross-links to neighboring areas in pure and applied mathematics
References
Recommended Textbooks