GraPHedron

GraPHedron. Interactive and Automated Conjectures in Extremal Graph Theory. GraPHedron is a conjecture-making system designed to help researchers in (extremal) graph theory. GraPHedron is the contraction of the words Graph and Polyhedron because its main principle is to view graphs as points in a space of selected invariants, in order to derive extremal properties among these invariants. GraPHedron is detailed in this paper. A dozen of published papers contain results that where first conjectured with the help of GraPHedron.


References in zbMATH (referenced in 15 articles )

Showing results 1 to 15 of 15.
Sorted by year (citations)

  1. Absil, Romain; Camby, Eglantine; Hertz, Alain; Mélot, Hadrien: A sharp lower bound on the number of non-equivalent colorings of graphs of order (n) and maximum degree (n - 3) (2018)
  2. Larson, C. E.; van Cleemput, N.: Automated conjecturing. III. Property-relations conjectures (2017)
  3. Hertz, Alain; Mélot, Hadrien: Counting the number of non-equivalent vertex colorings of a graph (2016)
  4. Hoppe, Travis; Petrone, Anna: Integer sequence discovery from small graphs (2016)
  5. Larson, C. E.; Van Cleemput, N.: Automated conjecturing. I: Fajtlowicz’s Dalmatian heuristic revisited (2016)
  6. Smith-Miles, Kate; Bowly, Simon: Generating new test instances by evolving in instance space (2015)
  7. Smith-Miles, Kate; Baatar, Davaatseren: Exploring the role of graph spectra in graph coloring algorithm performance (2014)
  8. Smith-Miles, Kate; Baatar, Davaatseren; Wreford, Brendan; Lewis, Rhyd: Towards objective measures of algorithm performance across instance space (2014)
  9. Bruyère, Véronique; Joret, Gwenaël; Mélot, Hadrien: Trees with given stability number and minimum number of stable sets (2012)
  10. Aouchiche, M.; Hansen, P.: A survey of automated conjectures in spectral graph theory (2010)
  11. Cardinal, Jean; Levy, Eythan: Connected vertex covers in dense graphs (2010)
  12. Bruyère, Véronique; Mélot, Hadrien: Fibonacci index and stability number of graphs: a polyhedral study (2009)
  13. Cardinal, Jean; Langerman, Stefan; Levy, Eythan: Improved approximation bounds for edge dominating set in dense graphs (2009)
  14. Christophe, Julie; Dewez, Sophie; Doignon, Jean-Paul; Fasbender, Gilles; Grégoire, Philippe; Huygens, David; Labbé, Martine; Elloumi, Sourour; Mélot, Hadrien; Yaman, Hande: Linear inequalities among graph invariants: using GraPHedron to uncover optimal relationships (2008)
  15. Mélot, Hadrien: Facet defining inequalities among graph invariants: The system graphedron (2008)