Skip to main content Accesibility Help
×
×
Home

Antisymmetrical Digraphs

  • W. T. Tutte (a1)
Summary

We call a digraph “antisymmetrical” if there is an automorphism θ of its graph, of period 2, which reverses the direction of every edge and maps no edge or vertex onto itself. We construct a theory of flows invariant under θ for such a diagraph. This theory is analogous to the Max Flow Min Cut theory for ordinary flows in digraphs. It is found to include that part of the theory of undirected graphs which discusses the existence of spanning subgraphs with a specified valency at each vertex.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Antisymmetrical Digraphs
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Antisymmetrical Digraphs
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Antisymmetrical Digraphs
      Available formats
      ×
Copyright
References
Hide All
1. Belck, H. B., Reguläre Faktoren von Graphen, J. Reine Angew. Math., 188 (1950), 228252.
2. Edmonds, J., Paths, trees and flowers, Can. J. Math., 17 (1965), 449467.
3. Ford, L. R. Jr., and Fulkerson, D. R., Flows in networks (Princeton, 1962).
4. Gallai, T., On factorization of graphs, Acta Math. Acad. Sci. Hungar., 1 (1950), 133153.
5. Gallai, T., Maximum-minimum Sätze una verallgemeinerte Faktoren von Graphen, Acta Math. Acad. Sci. Hungar., 12 (1961), 131173.
6. Ore, O., Graphs and subgraphs, I-II, Trans. Amer. Math. Soc., 84 (1957), 109136 and 93 (1959), 185-204.
7. Petersen, J., Die Theorie der regularen Graphs, Acta Math., 15 (1891), 193220.
8. Sainte-Lagüe, A., Les réseaux, Mém. Sci. Math. (Paris), 18 (1926).
9. Tutte, W. T., The factorization of linear graphs, J. London Math. Soc., 22 (1947), 107111.
10. Tutte, W. T., The factors of graphs, Can. J. Math., 4 (1952), 314328.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed