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05A Combinatorics: Enumerative combinatorics
05A05 Permutations, words, matrices
05A10 Factorials, binomial coefficients, combinatorial functions
05A15 Exact enumeration problems, generating functions
05A16 Asymptotic enumeration
05A17 Partitions of integers
05A18 Partitions of sets
05A19 Combinatorial identities, bijective combinatorics
05A20 Combinatorial inequalities
05A30 q-calculus and related topics
05A40 Umbral calculus
05A99 None of the above, but in this section
05B Combinatorics: Designs and configurations
05B05 Block designs
05B07 Triple systems
05B10 Difference sets (number-theoretic, group-theoretic, etc.)
05B15 Orthogonal arrays, Latin squares, Room squares
05B20 Matrices (incidence, Hadamard, etc.)
05B25 Finite geometries
05B30 Other designs, configurations
05B35 Matroids, geometric lattices
05B40 Packing and covering
05B45 Tessellation and tiling problems
05B50 Polyominoes
05B99 None of the above, but in this section
05C Combinatorics: Graph theory
05C05 Trees
05C07 Vertex degrees
05C10 Planar graphs; geometric and topological aspects of graph theory
05C12 Distance in graphs
05C15 Coloring of graphs and hypergraphs
05C17 Perfect graphs
05C20 Directed graphs (digraphs), tournaments
05C21 Flows in graphs
05C22 Signed and weighted graphs
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C30 Enumeration in graph theory
05C31 Graph polynomials
05C35 Extremal problems
05C38 Paths and cycles
05C40 Connectivity
05C42 Density (toughness, etc.)
05C45 Eulerian and Hamiltonian graphs
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C51 Graph designs and isomomorphic decomposition
05C55 Generalized Ramsey theory
05C57 Games on graphs
05C60 Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)
05C62 Graph representations (geometric and intersection representations, etc.) For graph drawing
05C63 Infinite graphs
05C65 Hypergraphs
05C69 Dominating sets, independent sets, cliques
05C70 Factorization, matching, partitioning, covering and packing
05C72 Fractional graph theory, fuzzy graph theory
05C75 Structural characterization of families of graphs
05C76 Graph operations (line graphs, products, etc.)
05C78 Graph labelling
05C80 Random graphs
05C81 Random walks on graphs
05C82 Small world graphs, complex networks
05C83 Graph minors
05C85 Graph algorithms
05C90 Applications
05C99 None of the above, but in this section
05 Combinatorics
05-00 General reference works
05-01 Instructional exposition
05-02 Research exposition
05-03 Historical
05-04 Explicit machine computation and programs
05-06 Proceedings, conferences, collections, etc.
05D Combinatorics: Extremal combinatorics
05D05 Extremal set theory
05D10 Ramsey theory
05D15 Transversal (matching) theory
05D40 Probabilistic methods
05D99 None of the above, but in this section
05E Combinatorics: Algebraic combinatorics
05E05 Symmetric functions and generalizations
05E10 Combinatorial aspects of representation theory
05E15 Combinatorial aspects of groups and algebras
05E18 Group actions on combinatorial structures
05E20 Group actions on designs, geometries and codes
05E25 Group actions on posets and homology groups of posets
05E30 Association schemes, strongly regular graphs
05E35 Orthogonal polynomials
05E40 Combinatorial aspects of commutative algebra
05E45 Combinatorial aspects of simplicial complexes
06B Order, lattices, ordered algebraic structures: Lattices
06B99 None of the above, but in this section
11B Sequences and sets
11B05 Density, gaps, topology
11H Number theory: Geometry of numbers
11H06 Lattices and convex bodies
11H71 Relations with coding theory
11T Number theory: Finite fields and commutative rings (number-theoretic aspects)
11T71 Algebraic coding theory; cryptography
13A Commutative algebra: General commutative ring theory
13A99 None of the above, but in this section
15A Linear and multilinear algebra; matrix theory: Basic linear algebra
15A15 Determinants, permanents, other special matrix functions
15A18 Eigenvalues, singular values, and eigenvectors
15B Linear and multilinear algebra; matrix theory: Special matrices
15B05 Toeplitz, Cauchy, and related matrices
16D Associative rings and algebras: Modules, bimodules and ideals
16D25 Ideals
20A Group theory and generalizations: Foundations
20A05 Axiomatics and elementary properties
20B Group theory and generalizations: Permutation groups
20B05 General theory for finite groups
20C Group theory and generalizations: Representation theory of groups
20C20 Modular representations and characters
20C99 None of the above, but in this section
20D Group theory and generalizations: Abstract finite groups
20D05 Finite simple groups and their classification
20D06 Simple groups: alternating groups and groups of Lie type
20D60 Arithmetic and combinatorial problems
60F Probability theory and stochastic processes: Limit theorems
60F05 Central limit and other weak theorems
Central limit and other weak theorems
68Q Computer science: Theory of computing
68Q25 Analysis of algorithms and problem complexity
68R Computer science: Discrete mathematics in relation to computer science
68R10 Graph theory (including graph drawing)
90C Operations research, mathematical programming: Mathematical programming
90C27 Combinatorial optimization
92E Biology and other natural sciences: Chemistry
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
93C Systems theory; control: Control systems
93C75 Applications of control theory
94B Information and communication, circuits: Theory of error-correcting codes and error-detecting codes
94B10 Convolutional codes
94B25 Combinatorial codes
94C Information and communication, circuits: Circuits, networks
94C15 Applications of graph theory
97K Mathematics education: Combinatorics, graph theory, probability theory, statistics
97K30 Graph theory
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