[seqfan] Fwd : House of Graphs: a database of interesting graphs -- an update

[Olivier Gerard]

This might be of interest to several seqfan members.

With my best regards,

Olivier Gérard



---------- Forwarded message ----------
From: Jan Goedgebeur <jan.goedgebeur at ugent.be>
Date: Tue, Feb 17, 2015 at 2:46 PM


Already in 2012 we announced the website "House of Graphs" --
http://hog.grinvin.org/ . In the meantime several new lists of graphs,
"interesting graphs", and invariants have been added to the website.

"House of Graphs" hosts lists of graphs (like Snarks, Fullerenes, etc.) and
links to other pages with lists of combinatorial structures (like vertex
transitive graphs, Ramsey graphs, etc.). But its main feature is a
searchable database of graphs that already occurred as counterexamples to
conjectures, as extremal graphs or in other contexts. In short we call this
the database of "interesting graphs".

The key idea is that although already for small vertex numbers extremely
many graphs exist, there are some that serve again and again as
counterexamples and that a database of these graphs should be established.
In this database one can e.g. search for graphs with certain invariant
values, graphs with a certain name (e.g. Petersen, Heawood, Balaban, etc.)
or graphs that are marked as being interesting for a certain invariant
(e.g. marked as being interesting for the girth). These searches can of
course also be combined and the results downloaded so that one gets good
candidates for testing new conjectures one is working on.

Users can also add graphs to the database. If the graphs are not yet in the
database, the system computes invariant values for the graphs. So the
database can also be used as a repository. If you discover new interesting
graphs, you can make them available to other users by submitting them to
the database together with a text identifier (e.g.
counterexample_this_conjecture).
Then other scientists can find and download the graph from "House of
Graphs".

More information on "House of Graphs" and its functionalities is given in:

Discrete Applied Mathematics, Volume 161, Issues 1-2, Jan. 2013, pages
311-314
Available online: http://dx.doi.org/10.1016/j.dam.2012.07.018

and

http://arxiv.org/abs/1204.3549

while "House of Graphs" can be accessed at: http://hog.grinvin.org/


Gunnar Brinkmann, Kris Coolsaet, Jan Goedgebeur and Hadrien Melot

-- 

Jan Goedgebeur
Applied Mathematics and Computer Science
Ghent University
Krijgslaan 281 - S9
B - 9000 Ghent