05C05 Trees
05C07 Degree sequences
05C10 Topological graph theory, imbedding [See also 57M15, 57M25]
05C12 Distance in graphs
05C15 Coloring of graphs and hypergraphs
05C17 Perfect graphs
05C20 Directed graphs (digraphs), tournaments
05C22 Signed, gain and biased graphs
05C25 Graphs and groups [See also 20F65]
05C30 Enumeration of graphs and maps
05C35 Extremal problems [See also 90C35]
05C38 Paths and cycles [See also 90B10]
05C40 Connectivity
05C45 Eulerian and Hamiltonian graphs
05C50 Graphs and matrices
05C55 Generalized Ramsey theory
05C60 Isomorphism problems (reconstruction conjecture, etc.)
05C62 Graph representations (geometric and intersection representations, etc.)
05C65 Hypergraphs
05C69 Dominating sets, independent sets, cliques
05C70 Factorization, matching, covering and packing
05C75 Structural characterization of types of graphs
05C78 Graph labelling (graceful graphs, bandwidth, etc.)
05C80 Random graphs
05C83 Graph minors
05C85 Graph algorithms [See also 68R10, 68W05]
05C90 Applications
05C99 None of the above, but in this section