Tuesday, February 17, 2015

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

Already in 2012 we announced the website "House of Graphs" --
http://hog.grinvin.org/ -- through this mailing list. 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
Available online: http://dx.doi.org/10.1016/j.dam.2012.07.018



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

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