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Mathematics Subject Classification – MSC2010

05-XX

Combinatorics [For finite fields, see 11Txx] 161887

05-00

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

05-01

Instructional exposition (textbooks, tutorial papers, etc.) 848

05-02

Research exposition (monographs, survey articles) 1536

05-03

Historical (must also be assigned at least one classification number from Section 01) 386

05-04

Explicit machine computation and programs (not the theory of computation or programming) 745

05-06

Proceedings, conferences, collections, etc. 1403

05Axx

Enumerative combinatorics [For enumeration in graph theory, see 05C30] 23119

05A05

Permutations, words, matrices 5426

05A10

Factorials, binomial coefficients, combinatorial functions [See also 11B65, 33Cxx] 2798

05A15

Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 8739

05A16

Asymptotic enumeration 1087

05A17

Partitions of integers [See also 11P81, 11P82, 11P83] 3299

05A18

Partitions of sets 1132

05A19

Combinatorial identities, bijective combinatorics 3742

05A20

Combinatorial inequalities 674

05A30

$q$-calculus and related topics [See also 33Dxx] 1291

05A40

Umbral calculus 389

05A99

None of the above, but in this section 1183

05Bxx

Designs and configurations [For applications of design theory, see 94C30] 26891

05B05

Block designs [See also 51E05, 62K10] 5930

05B07

Triple systems 1508

05B10

Difference sets (number-theoretic, group-theoretic, etc.) [See also 11B13] 1590

05B15

Orthogonal arrays, Latin squares, Room squares 3852

05B20

Matrices (incidence, Hadamard, etc.) 3609

05B25

Finite geometries [See also 51D20, 51Exx] 3139

05B30

Other designs, configurations [See also 51E30] 3478

05B35

Matroids, geometric lattices [See also 52B40, 90C27] 4032

05B40

Packing and covering [See also 11H31, 52C15, 52C17] 1915

05B45

Tessellation and tiling problems [See also 52C20, 52C22] 1527

05B50

Polyominoes 553

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] 109969

05C05

Trees 10427

05C07

Vertex degrees [See also 05E30] 2109

05C10

Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25] 9717

05C12

Distance in graphs 5737

05C15

Coloring of graphs and hypergraphs 14306

05C17

Perfect graphs 433

05C20

Directed graphs (digraphs), tournaments 8667

05C21

Flows in graphs 359

05C22

Signed and weighted graphs 1256

05C25

Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65] 7823

05C30

Enumeration in graph theory 3645

05C31

Graph polynomials 837

05C35

Extremal problems [See also 90C35] 12029

05C38

Paths and cycles [See also 90B10] 10450

05C40

Connectivity 5964

05C42

Density (toughness, etc.) 394

05C45

Eulerian and Hamiltonian graphs 4614

05C50

Graphs and linear algebra (matrices, eigenvalues, etc.) 8742

05C51

Graph designs and isomomorphic decomposition [See also 05B30] 261

05C55

Generalized Ramsey theory [See also 05D10] 2114

05C57

Games on graphs [See also 91A43, 91A46] 665

05C60

Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) 2600

05C62

Graph representations (geometric and intersection representations, etc.) [For graph drawing, see also 68R10] 2067

05C63

Infinite graphs 425

05C65

Hypergraphs 4258

05C69

Dominating sets, independent sets, cliques 6397

05C70

Factorization, matching, partitioning, covering and packing 11050

05C72

Fractional graph theory, fuzzy graph theory 321

05C75

Structural characterization of families of graphs 4562

05C76

Graph operations (line graphs, products, etc.) 1854

05C78

Graph labelling (graceful graphs, bandwidth, etc.) 4094

05C80

Random graphs [See also 60B20] 5117

05C81

Random walks on graphs 642

05C82

Small world graphs, complex networks [See also 90Bxx, 91D30] 1751

05C83

Graph minors 738

05C85

Graph algorithms [See also 68R10, 68W05] 11564

05C90

Applications [See also 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15] 5857

05C99

None of the above, but in this section 7702

05Dxx

Extremal combinatorics 3609

05D05

Extremal set theory 1371

05D10

Ramsey theory [See also 05C55] 1524

05D15

Transversal (matching) theory 249

05D40

Probabilistic methods 350

05D99

None of the above, but in this section 243

05Exx

Algebraic combinatorics 10118

05E05

Symmetric functions and generalizations 2339

05E10

Combinatorial aspects of representation theory [See also 20C30] 2948

05E15

Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80] 1663

05E18

Group actions on combinatorial structures 400

05E30

Association schemes, strongly regular graphs 2028

05E40

Combinatorial aspects of commutative algebra 349

05E45

Combinatorial aspects of simplicial complexes 514

05E99

None of the above, but in this section 510

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cc	classification code
ct	classification text

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!ab	logic not	(ab c)	parentheses

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Mathematics Subject Classification – MSC2010

Overview