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Mathematics Subject Classification – MSC2010

05-XX

Combinatorics [For finite fields, see 11Txx] 166431

05-00

General reference works (handbooks, dictionaries, bibliographies, etc.) 23

05-01

Instructional exposition (textbooks, tutorial papers, etc.) 864

05-02

Research exposition (monographs, survey articles) 1550

05-03

Historical (must also be assigned at least one classification number from Section 01) 391

05-04

Explicit machine computation and programs (not the theory of computation or programming) 755

05-06

Proceedings, conferences, collections, etc. 1429

05Axx

Enumerative combinatorics [For enumeration in graph theory, see 05C30] 23720

05A05

Permutations, words, matrices 5586

05A10

Factorials, binomial coefficients, combinatorial functions [See also 11B65, 33Cxx] 2860

05A15

Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 8959

05A16

Asymptotic enumeration 1118

05A17

Partitions of integers [See also 11P81, 11P82, 11P83] 3419

05A18

Partitions of sets 1174

05A19

Combinatorial identities, bijective combinatorics 3862

05A20

Combinatorial inequalities 689

05A30

$q$-calculus and related topics [See also 33Dxx] 1340

05A40

Umbral calculus 397

05A99

None of the above, but in this section 1182

05Bxx

Designs and configurations [For applications of design theory, see 94C30] 27247

05B05

Block designs [See also 51E05, 62K10] 5983

05B07

Triple systems 1525

05B10

Difference sets (number-theoretic, group-theoretic, etc.) [See also 11B13] 1608

05B15

Orthogonal arrays, Latin squares, Room squares 3898

05B20

Matrices (incidence, Hadamard, etc.) 3641

05B25

Finite geometries [See also 51D20, 51Exx] 3180

05B30

Other designs, configurations [See also 51E30] 3504

05B35

Matroids, geometric lattices [See also 52B40, 90C27] 4120

05B40

Packing and covering [See also 11H31, 52C15, 52C17] 1947

05B45

Tessellation and tiling problems [See also 52C20, 52C22] 1564

05B50

Polyominoes 560

05B99

None of the above, but in this section 611

05Cxx

Graph theory [For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15] 113165

05C05

Trees 10651

05C07

Vertex degrees [See also 05E30] 2211

05C10

Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25] 9965

05C12

Distance in graphs 5997

05C15

Coloring of graphs and hypergraphs 14693

05C17

Perfect graphs 443

05C20

Directed graphs (digraphs), tournaments 8872

05C21

Flows in graphs 388

05C22

Signed and weighted graphs 1322

05C25

Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65] 8031

05C30

Enumeration in graph theory 3750

05C31

Graph polynomials 901

05C35

Extremal problems [See also 90C35] 12220

05C38

Paths and cycles [See also 90B10] 10681

05C40

Connectivity 6173

05C42

Density (toughness, etc.) 425

05C45

Eulerian and Hamiltonian graphs 4708

05C50

Graphs and linear algebra (matrices, eigenvalues, etc.) 9043

05C51

Graph designs and isomomorphic decomposition [See also 05B30] 269

05C55

Generalized Ramsey theory [See also 05D10] 2144

05C57

Games on graphs [See also 91A43, 91A46] 702

05C60

Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) 2705

05C62

Graph representations (geometric and intersection representations, etc.) [For graph drawing, see also 68R10] 2141

05C63

Infinite graphs 454

05C65

Hypergraphs 4407

05C69

Dominating sets, independent sets, cliques 6693

05C70

Factorization, matching, partitioning, covering and packing 11352

05C72

Fractional graph theory, fuzzy graph theory 348

05C75

Structural characterization of families of graphs 4643

05C76

Graph operations (line graphs, products, etc.) 1969

05C78

Graph labelling (graceful graphs, bandwidth, etc.) 4207

05C80

Random graphs [See also 60B20] 5320

05C81

Random walks on graphs 698

05C82

Small world graphs, complex networks [See also 90Bxx, 91D30] 1971

05C83

Graph minors 773

05C85

Graph algorithms [See also 68R10, 68W05] 12006

05C90

Applications [See also 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15] 6113

05C99

None of the above, but in this section 7737

05Dxx

Extremal combinatorics 3742

05D05

Extremal set theory 1407

05D10

Ramsey theory [See also 05C55] 1583

05D15

Transversal (matching) theory 259

05D40

Probabilistic methods 372

05D99

None of the above, but in this section 253

05Exx

Algebraic combinatorics 10609

05E05

Symmetric functions and generalizations 2457

05E10

Combinatorial aspects of representation theory [See also 20C30] 3093

05E15

Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80] 1770

05E18

Group actions on combinatorial structures 429

05E30

Association schemes, strongly regular graphs 2081

05E40

Combinatorial aspects of commutative algebra 382

05E45

Combinatorial aspects of simplicial complexes 562

05E99

None of the above, but in this section 530

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Mathematics Subject Classification – MSC2010

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