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Mathematical Sciences Classification System

05Cxx - Graph theory
{For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15}

• 16
  05C05
  Trees
• 2
  05C07
  Vertex degrees [See also 05E30]
• 12
  05C10
  Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]
• 5
  05C12
  Distance in graphs
• 19
  05C15
  Coloring of graphs and hypergraphs
• 2
  05C17
  Perfect graphs
• 8
  05C20
  Directed graphs (digraphs), tournaments
• 05C21
  Flows in graphs
• 05C22
  Signed and weighted graphs
• 22
  05C25
  Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65]
• 5
  05C30
  Enumeration in graph theory
• 4
  05C31
  Graph polynomials
• 8
  05C35
  Extremal problems [See also 90C35]
• 3
  05C38
  Paths and cycles [See also 90B10]
• 3
  05C40
  Connectivity
• 2
  05C42
  Density (toughness, etc.)
• 5
  05C45
  Eulerian and Hamiltonian graphs
• 31
  05C50
  Graphs and linear algebra (matrices, eigenvalues, etc.)
• 05C51
  Graph designs and isomomorphic decomposition [See also 05B30]
• 4
  05C55
  Generalized Ramsey theory [See also 05D10]
• 4
  05C57
  Games on graphs [See also 91A43, 91A46]
• 3
  05C60
  Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)
• 1
  05C62
  Graph representations (geometric and intersection representations, etc.) {For graph drawing, see also 68R10}
• 2
  05C63
  Infinite graphs
• 8
  05C65
  Hypergraphs
• 1
  05C69
  Dominating sets, independent sets, cliques
• 5
  05C70
  Factorization, matching, partitioning, covering and packing
• 1
  05C72
  Fractional graph theory, fuzzy graph theory
• 2
  05C75
  Structural characterization of families of graphs
• 1
  05C76
  Graph operations (line graphs, products, etc.)
• 3
  05C78
  Graph labelling (graceful graphs, bandwidth, etc.)
• 30
  05C80
  Random graphs [See also 60B20]
• 13
  05C81
  Random walks on graphs
• 5
  05C82
  Small world graphs, complex networks [See also 90Bxx, 91D30]
• 05C83
  Graph minors
• 14
  05C85
  Graph algorithms [See also 68R10, 68W05]
• 20
  05C90
  Applications [See also 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15]
• 1
  05C99
  None of the above, but in this section