Amendments to some subgraph tabulations of Steinbach |
Peter Steinbach's useful Field Guide to Simple Graphs is marred by a few sporadic errors in its lists of spanning subgraphs and supergraphs for graphs on 5, 6 or 7 vertices. We have produced a comprehensive collection of amendments to his tabulations. With the inclusion of these amendments, his lists can be used with confidence. This is joint work by Peter Adams (University of Queensland), Roger Eggleton (Illinois State University), James MacDougall (University of Newcastle) and Ebadollah Mahmoodian (Sharif University of Technology).
This paper has now appeared in Bull. Inst. Combin. Appl. 37 (2003), 29-34.
Here is the paper in three formats. For a description and summary of the results, and a short list of references, please read it via one of these links.
The paper implicitly lists and corrects only the erroneous portions in Steinbach's tables of spanning subgraphs and supergraphs. For convenience, we give the following files which fully specify the spanning subgraph/supergraph relationships for graphs on 5, 6 or 7 vertices. Thus these files reproduce the tables in Steinbach's Field Guide to Simple Graphs, but with the errors amended. Note that we use the same numbering scheme as he does.
For readers who do not have on hand a copy of Steinbach's Field Guide to Simple Graphs, we have also created text files which contain information about the graphs. Corresponding to each Steinbach reference number we give the degree sequence of the graph and list its edge set.