Automated and computer assisted conjectures in graph theory

• Account
• GraPHedron's basics
• Invariants and graph's classes
• Online bibliography
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welcome

GraPHedron is a computer-assisted system which helps to obtain conjectures in graph theory. It uses a polyhedral approach to find strongest relations among graph invariants. This approach provides a formal framework allowing to identify interesting and tight relations.

If it is your first visit, please learn the basics of GraPHedron to understand what it can do, in order to help you in your graph theory research. Otherwise, please log in and start to work with GraPHedron.

Latest news

• Friday 26 October 2007: The paper explaining the principles of GraPHedron is available

  The paper Facet defining inequalities among graph invariants: the system GraPHedron to appear in Discrete Applied Mathematics is now available online. You can download it via ScienceDirect.

• Monday 23 April 2007: Lemon C++ Library allowed in invariant's implementation

  You can now request a new invariant providing an implementation which uses the Lemon C++ library version 0.6 (Library of Efficient Models and Optimization in Networks) in the ask new invariant page.
  Such requests can be very quickly treated as their implementations can be directly added to the system.
  Moreover, this library is very efficient and intended to grow quickly.

• Friday 30 March 2007: Real invariants allowed

  You can now use invariants with real values (often from spectral or chemical graph theory, see the list of real invariants).
  However, you have to be aware that in this case:
    - computation is approximated (floating point arithmetic)
    - the number of polytope's vertices can be huge (it can be useful to deselect the point's distribution option)

See all news.

Notice

This web portal of GraPHedron allows you to use a specific version of the system. There are some differences between this version and the console version of GraPHedron:

• All graphs and invariants data are precomputed. It means that solving a problem is more fast but it implies that the usable data must be already computed. The GraPHedron server is continuously computing new data which are then added to the available classes of graphs and invariants.
• All console options are not available at this time. New options are added regularily to the web version, after a testing phase.