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Mathematics Subject Classification – MSC2010

05-XX

Combinatorics [For finite fields, see 11Txx] 164854

05-00

General reference works (handbooks, dictionaries, bibliographies, etc.) 22

05-01

Instructional exposition (textbooks, tutorial papers, etc.) 853

05-02

Research exposition (monographs, survey articles) 1543

05-03

Historical (must also be assigned at least one classification number from Section 01) 388

05-04

Explicit machine computation and programs (not the theory of computation or programming) 751

05-06

Proceedings, conferences, collections, etc. 1418

05Axx

Enumerative combinatorics [For enumeration in graph theory, see 05C30] 23517

05A05

Permutations, words, matrices 5536

05A10

Factorials, binomial coefficients, combinatorial functions [See also 11B65, 33Cxx] 2839

05A15

Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 8884

05A16

Asymptotic enumeration 1107

05A17

Partitions of integers [See also 11P81, 11P82, 11P83] 3388

05A18

Partitions of sets 1163

05A19

Combinatorial identities, bijective combinatorics 3818

05A20

Combinatorial inequalities 684

05A30

$q$-calculus and related topics [See also 33Dxx] 1321

05A40

Umbral calculus 395

05A99

None of the above, but in this section 1182

05Bxx

Designs and configurations [For applications of design theory, see 94C30] 27134

05B05

Block designs [See also 51E05, 62K10] 5968

05B07

Triple systems 1522

05B10

Difference sets (number-theoretic, group-theoretic, etc.) [See also 11B13] 1602

05B15

Orthogonal arrays, Latin squares, Room squares 3883

05B20

Matrices (incidence, Hadamard, etc.) 3633

05B25

Finite geometries [See also 51D20, 51Exx] 3171

05B30

Other designs, configurations [See also 51E30] 3500

05B35

Matroids, geometric lattices [See also 52B40, 90C27] 4093

05B40

Packing and covering [See also 11H31, 52C15, 52C17] 1935

05B45

Tessellation and tiling problems [See also 52C20, 52C22] 1548

05B50

Polyominoes 557

05B99

None of the above, but in this section 608

05Cxx

Graph theory [For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15] 112019

05C05

Trees 10564

05C07

Vertex degrees [See also 05E30] 2170

05C10

Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25] 9878

05C12

Distance in graphs 5900

05C15

Coloring of graphs and hypergraphs 14585

05C17

Perfect graphs 443

05C20

Directed graphs (digraphs), tournaments 8784

05C21

Flows in graphs 378

05C22

Signed and weighted graphs 1301

05C25

Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65] 7947

05C30

Enumeration in graph theory 3715

05C31

Graph polynomials 875

05C35

Extremal problems [See also 90C35] 12146

05C38

Paths and cycles [See also 90B10] 10612

05C40

Connectivity 6092

05C42

Density (toughness, etc.) 416

05C45

Eulerian and Hamiltonian graphs 4671

05C50

Graphs and linear algebra (matrices, eigenvalues, etc.) 8931

05C51

Graph designs and isomomorphic decomposition [See also 05B30] 268

05C55

Generalized Ramsey theory [See also 05D10] 2134

05C57

Games on graphs [See also 91A43, 91A46] 692

05C60

Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) 2671

05C62

Graph representations (geometric and intersection representations, etc.) [For graph drawing, see also 68R10] 2121

05C63

Infinite graphs 442

05C65

Hypergraphs 4362

05C69

Dominating sets, independent sets, cliques 6598

05C70

Factorization, matching, partitioning, covering and packing 11267

05C72

Fractional graph theory, fuzzy graph theory 332

05C75

Structural characterization of families of graphs 4626

05C76

Graph operations (line graphs, products, etc.) 1921

05C78

Graph labelling (graceful graphs, bandwidth, etc.) 4176

05C80

Random graphs [See also 60B20] 5244

05C81

Random walks on graphs 680

05C82

Small world graphs, complex networks [See also 90Bxx, 91D30] 1857

05C83

Graph minors 763

05C85

Graph algorithms [See also 68R10, 68W05] 11869

05C90

Applications [See also 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15] 5981

05C99

None of the above, but in this section 7730

05Dxx

Extremal combinatorics 3696

05D05

Extremal set theory 1388

05D10

Ramsey theory [See also 05C55] 1564

05D15

Transversal (matching) theory 259

05D40

Probabilistic methods 366

05D99

None of the above, but in this section 251

05Exx

Algebraic combinatorics 10431

05E05

Symmetric functions and generalizations 2405

05E10

Combinatorial aspects of representation theory [See also 20C30] 3040

05E15

Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80] 1722

05E18

Group actions on combinatorial structures 421

05E30

Association schemes, strongly regular graphs 2063

05E40

Combinatorial aspects of commutative algebra 370

05E45

Combinatorial aspects of simplicial complexes 548

05E99

None of the above, but in this section 524

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ct	classification text

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Mathematics Subject Classification – MSC2010

Overview