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Mathematics Subject Classification – MSC2010

05-XX

Combinatorics [For finite fields, see 11Txx] 163521

05-00

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

05-01

Instructional exposition (textbooks, tutorial papers, etc.) 851

05-02

Research exposition (monographs, survey articles) 1537

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) 747

05-06

Proceedings, conferences, collections, etc. 1413

05Axx

Enumerative combinatorics [For enumeration in graph theory, see 05C30] 23315

05A05

Permutations, words, matrices 5479

05A10

Factorials, binomial coefficients, combinatorial functions [See also 11B65, 33Cxx] 2821

05A15

Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 8819

05A16

Asymptotic enumeration 1095

05A17

Partitions of integers [See also 11P81, 11P82, 11P83] 3345

05A18

Partitions of sets 1144

05A19

Combinatorial identities, bijective combinatorics 3773

05A20

Combinatorial inequalities 678

05A30

$q$-calculus and related topics [See also 33Dxx] 1305

05A40

Umbral calculus 390

05A99

None of the above, but in this section 1182

05Bxx

Designs and configurations [For applications of design theory, see 94C30] 27023

05B05

Block designs [See also 51E05, 62K10] 5954

05B07

Triple systems 1516

05B10

Difference sets (number-theoretic, group-theoretic, etc.) [See also 11B13] 1596

05B15

Orthogonal arrays, Latin squares, Room squares 3865

05B20

Matrices (incidence, Hadamard, etc.) 3621

05B25

Finite geometries [See also 51D20, 51Exx] 3156

05B30

Other designs, configurations [See also 51E30] 3492

05B35

Matroids, geometric lattices [See also 52B40, 90C27] 4063

05B40

Packing and covering [See also 11H31, 52C15, 52C17] 1924

05B45

Tessellation and tiling problems [See also 52C20, 52C22] 1538

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] 111077

05C05

Trees 10507

05C07

Vertex degrees [See also 05E30] 2136

05C10

Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25] 9816

05C12

Distance in graphs 5827

05C15

Coloring of graphs and hypergraphs 14473

05C17

Perfect graphs 439

05C20

Directed graphs (digraphs), tournaments 8732

05C21

Flows in graphs 366

05C22

Signed and weighted graphs 1276

05C25

Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65] 7903

05C30

Enumeration in graph theory 3685

05C31

Graph polynomials 865

05C35

Extremal problems [See also 90C35] 12096

05C38

Paths and cycles [See also 90B10] 10545

05C40

Connectivity 6035

05C42

Density (toughness, etc.) 404

05C45

Eulerian and Hamiltonian graphs 4645

05C50

Graphs and linear algebra (matrices, eigenvalues, etc.) 8847

05C51

Graph designs and isomomorphic decomposition [See also 05B30] 264

05C55

Generalized Ramsey theory [See also 05D10] 2125

05C57

Games on graphs [See also 91A43, 91A46] 683

05C60

Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) 2642

05C62

Graph representations (geometric and intersection representations, etc.) [For graph drawing, see also 68R10] 2100

05C63

Infinite graphs 434

05C65

Hypergraphs 4318

05C69

Dominating sets, independent sets, cliques 6513

05C70

Factorization, matching, partitioning, covering and packing 11167

05C72

Fractional graph theory, fuzzy graph theory 326

05C75

Structural characterization of families of graphs 4599

05C76

Graph operations (line graphs, products, etc.) 1885

05C78

Graph labelling (graceful graphs, bandwidth, etc.) 4144

05C80

Random graphs [See also 60B20] 5182

05C81

Random walks on graphs 661

05C82

Small world graphs, complex networks [See also 90Bxx, 91D30] 1811

05C83

Graph minors 753

05C85

Graph algorithms [See also 68R10, 68W05] 11724

05C90

Applications [See also 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15] 5905

05C99

None of the above, but in this section 7718

05Dxx

Extremal combinatorics 3652

05D05

Extremal set theory 1381

05D10

Ramsey theory [See also 05C55] 1547

05D15

Transversal (matching) theory 251

05D40

Probabilistic methods 359

05D99

None of the above, but in this section 247

05Exx

Algebraic combinatorics 10306

05E05

Symmetric functions and generalizations 2384

05E10

Combinatorial aspects of representation theory [See also 20C30] 3002

05E15

Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80] 1695

05E18

Group actions on combinatorial structures 408

05E30

Association schemes, strongly regular graphs 2053

05E40

Combinatorial aspects of commutative algebra 365

05E45

Combinatorial aspects of simplicial complexes 530

05E99

None of the above, but in this section 518

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cc	classification code
ct	classification text

a & b	logic and	abc*	right wildcard
a \| b	logic or	"ab c"	phrase
!ab	logic not	(ab c)	parentheses

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Mathematics Subject Classification – MSC2010

Overview