Limit points for average genus. II: 2-connected non-simplicial graphs
The average genus of a graph \(G\) is the average value of the genus of the imbedding surface, taken over all orientable embeddings of \(G\). Given a collection of graphs, the authors consider the set of values of the average genus of these graphs; specifically, does this set have a limit point? The idea behind the question is how well does the average value serve to distinguish between graphs in the collection. In Part I of this paper [ibid., Ser. B 55, No. 1, 83-103 (1992; Zbl 0709.05017)] the authors proved that there are no limit points for the average genus of 2- connected simplicial (simple) graph or for the average genus of 3- connected graphs. In this paper the authors give a systematic method for constructing sequences of 2-connected nonsimplicial graphs whose average genus converges to a limit point. Their construction involves a variation on necklaces, which have been used before in this context. They also prove that their method is in a sense unique.
scientific article; zbMATH DE number 130564
scientific article