Random Graphs from Restricted Classes
نویسندگان
چکیده
A block in a graph G is a maximal subgraph with no cut-vertex. Blocks are either 2-connected graphs, or the graph with two vertices and only one edge, or, in the case where G is just a single vertex, G itself. Definition 1.1. Let C be a class of connected graphs, and B ⊆ C the class of 2-connected graphs in C (B may contain the graph formed by an edge). We call C stable if it satisfies the following properties: (i) let C ∈ C and B ∈ B. Then the graph obtained by identifying any vertex of C with any vertex of B and relabeling it so that it is well-labeled in C. (ii) All C ∈ C \ B can be constructed as in (i). (iii) The single vertex graph is an element of C. (iv) B is closed under permutation of labels. A few examples are: • C = the class of trees, with B the class with only one edge. • C = the class of planar graphs: B consists of all 2-connected planar graphs, together with the graph consisting of a single edge. • C = the class of outerplanar graphs: B consists of all 2-connected outerplanar graphs (dissection of polygons).
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