Title: PHOEG Helps Obtaining Extremal Graphs,
Abstract: Extremal Graph Theory aims to determine bounds for graph invariants as well
as the graphs attaining those bounds.
We are currently developping PHOEG, an ecosystem of tools designed to help
researchers in Extremal Graph Theory.
It uses a big relational database of undirected graphs and works with the
convex hull of the graphs as points in the invariants space in order to exactly
obtain the extremal graphs and optimal bounds on the invariants for some fixed
parameters. The results obtained on the restricted finite class of graphs can
later be used to infer conjectures. This database also allows us to make
queries on those graphs. Once the conjecture defined, PHOEG goes one step
further by helping in the process of designing a proof guided by successive
applications of transformations from any graph to an extremal graph. To this
aim, we use a second database based on a graph data model.
The paper presents ideas and techniques used in PHOEG to assist the study of
Extremal Graph Theory.