05XX 


Combinatorics {For finite fields, see 11Txx} 

05Cxx 

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


05C05 
Trees 


05C07 
Vertex degrees [See also 05E30] 


05C10 
Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25] 


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.) [See also 20F65] 


05C30 
Enumeration in graph theory 


05C31 
Graph polynomials 


05C35 
Extremal problems [See also 90C35] 


05C38 
Paths and cycles [See also 90B10] 


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 [See also 05B30] 


05C55 
Generalized Ramsey theory [See also 05D10] 


05C57 
Games on graphs [See also 91A43, 91A46] 


05C60 
Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) 


05C62 
Graph representations (geometric and intersection representations, etc.) {For graph drawing, see also 68R10} 


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 (graceful graphs, bandwidth, etc.) 


05C80 
Random graphs [See also 60B20] 


05C81 
Random walks on graphs 


05C82 
Small world graphs, complex networks [See also 90Bxx, 91D30] 


05C83 
Graph minors 


05C85 
Graph algorithms [See also 68R10, 68W05] 


05C90 
Applications [See also 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15] 


05C99 
None of the above, but in this section 