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Mathematics Subject Classification – MSC2010

05-XX

Combinatorics [For finite fields, see 11Txx] 168771

05-00

General reference works (handbooks, dictionaries, bibliographies, etc.) 24

05-01

Instructional exposition (textbooks, tutorial papers, etc.) 874

05-02

Research exposition (monographs, survey articles) 1556

05-03

Historical (must also be assigned at least one classification number from Section 01) 395

05-04

Explicit machine computation and programs (not the theory of computation or programming) 756

05-06

Proceedings, conferences, collections, etc. 1433

05Axx

Enumerative combinatorics [For enumeration in graph theory, see 05C30] 24027

05A05

Permutations, words, matrices 5671

05A10

Factorials, binomial coefficients, combinatorial functions [See also 11B65, 33Cxx] 2909

05A15

Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 9073

05A16

Asymptotic enumeration 1131

05A17

Partitions of integers [See also 11P81, 11P82, 11P83] 3452

05A18

Partitions of sets 1192

05A19

Combinatorial identities, bijective combinatorics 3936

05A20

Combinatorial inequalities 695

05A30

$q$-calculus and related topics [See also 33Dxx] 1357

05A40

Umbral calculus 400

05A99

None of the above, but in this section 1185

05Bxx

Designs and configurations [For applications of design theory, see 94C30] 27439

05B05

Block designs [See also 51E05, 62K10] 6007

05B07

Triple systems 1532

05B10

Difference sets (number-theoretic, group-theoretic, etc.) [See also 11B13] 1629

05B15

Orthogonal arrays, Latin squares, Room squares 3922

05B20

Matrices (incidence, Hadamard, etc.) 3669

05B25

Finite geometries [See also 51D20, 51Exx] 3197

05B30

Other designs, configurations [See also 51E30] 3522

05B35

Matroids, geometric lattices [See also 52B40, 90C27] 4168

05B40

Packing and covering [See also 11H31, 52C15, 52C17] 1955

05B45

Tessellation and tiling problems [See also 52C20, 52C22] 1581

05B50

Polyominoes 567

05B99

None of the above, but in this section 612

05Cxx

Graph theory [For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15] 114846

05C05

Trees 10759

05C07

Vertex degrees [See also 05E30] 2278

05C10

Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25] 10093

05C12

Distance in graphs 6125

05C15

Coloring of graphs and hypergraphs 14885

05C17

Perfect graphs 453

05C20

Directed graphs (digraphs), tournaments 8978

05C21

Flows in graphs 394

05C22

Signed and weighted graphs 1360

05C25

Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65] 8131

05C30

Enumeration in graph theory 3812

05C31

Graph polynomials 937

05C35

Extremal problems [See also 90C35] 12328

05C38

Paths and cycles [See also 90B10] 10780

05C40

Connectivity 6274

05C42

Density (toughness, etc.) 442

05C45

Eulerian and Hamiltonian graphs 4761

05C50

Graphs and linear algebra (matrices, eigenvalues, etc.) 9182

05C51

Graph designs and isomomorphic decomposition [See also 05B30] 274

05C55

Generalized Ramsey theory [See also 05D10] 2170

05C57

Games on graphs [See also 91A43, 91A46] 729

05C60

Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) 2735

05C62

Graph representations (geometric and intersection representations, etc.) [For graph drawing, see also 68R10] 2176

05C63

Infinite graphs 465

05C65

Hypergraphs 4466

05C69

Dominating sets, independent sets, cliques 6844

05C70

Factorization, matching, partitioning, covering and packing 11488

05C72

Fractional graph theory, fuzzy graph theory 376

05C75

Structural characterization of families of graphs 4703

05C76

Graph operations (line graphs, products, etc.) 2015

05C78

Graph labelling (graceful graphs, bandwidth, etc.) 4258

05C80

Random graphs [See also 60B20] 5433

05C81

Random walks on graphs 722

05C82

Small world graphs, complex networks [See also 90Bxx, 91D30] 2134

05C83

Graph minors 797

05C85

Graph algorithms [See also 68R10, 68W05] 12247

05C90

Applications [See also 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15] 6269

05C99

None of the above, but in this section 7756

05Dxx

Extremal combinatorics 3825

05D05

Extremal set theory 1434

05D10

Ramsey theory [See also 05C55] 1625

05D15

Transversal (matching) theory 266

05D40

Probabilistic methods 378

05D99

None of the above, but in this section 258

05Exx

Algebraic combinatorics 10807

05E05

Symmetric functions and generalizations 2500

05E10

Combinatorial aspects of representation theory [See also 20C30] 3154

05E15

Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80] 1813

05E18

Group actions on combinatorial structures 442

05E30

Association schemes, strongly regular graphs 2106

05E40

Combinatorial aspects of commutative algebra 396

05E45

Combinatorial aspects of simplicial complexes 583

05E99

None of the above, but in this section 537

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ct	classification text

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Mathematics Subject Classification – MSC2010

Overview