Enumerating $2$-cell imbeddings of connected graphs

Enumerating 2-cell Imbeddings of Connected Graphs

A systematic approach is developed for enumerating congruence classes of 2-cell imbeddings of connected graphs on closed orientable 2-manifolds. The method is applied to the wheel graphs and to the complete graphs. Congruence class genus polynomials and congruence class imbedding polynomials are introduced, to summarize important information refining the enumeration.

Enumerating the orientable 2-cell imbeddings of complete bipartite graphs

Asymptotic expansions for enumerating connected labelled graphs

I compute several terms of the asymptotic expansion of the number of connected labelled graphs with n nodes and m edges, for small k = m−n. I thus identify an error in a recent paper of Flajolet et al.

Enumerating Minimal Connected Dominating Sets in Graphs of Bounded Chordality

Listing, generating or enumerating objects of specified type is one of the principal tasks in algorithmics. In graph algorithms one often enumerates vertex subsets satisfying a certain property. We study the enumeration of all minimal connected dominating sets of an input graph from various graph classes of bounded chordality. We establish enumeration algorithms as well as lower and upper bound...

Enumerating Spanning and Connected Subsets in Graphs and Matroids

We show that enumerating all minimal spanning and connected subsets of a given matroid can be solved in incremental quasipolynomial time. In the special case of graphical matroids, we improve this complexity bound by showing that all minimal 2-vertex connected edge subsets of a given graph can be generated in incremental polynomial time.