Maximal Planar graphs with minimal degree five
MPG5 and C3-5 planar triangulations
Philippe Rolland
Doctor (Ph. D Thesis in Computer Science, Ecole Central de Nantes), Major CNRS competition 2001, 3er World Champion Ship JavaCup¹98
See Resume/cv

1. In progress : New Approach to construct $MPG5$.
2. Tools to compare, test and search MPG5 particularities by starting with PLANTRI.
3. About 4CT: Another formulation of the Four Color Theorem
4. Conferences : ISICT 06/2003 | SIAM Discrete Mathematics 08/2002

1. Around Flip and Explosion.
We are looking for a new approach in order to construct all $MPG5$. Here we will give some informations about this goal.

2. Around plantri.
We have running PLANTRI (The authors are Gunnar Brinkmann (University of Bielefeld) and Brendan McKay (Australian National University) : This soft can be found at with the following command line "plantri40 -c3 -m5 20 -a file.txt", see command line for 17 to 26 vertices. All no-isomorphic graphs have been stored in MySql database in order to compute without restriction, all tests.

3. About 4CT: Four Color Theorem, another formulation(Nov. 5, 2002)

sometimes "It is necessary to complicate a problem to simplify
the solution of it" (Erdös) 

The theorem of the four colors is a
particular case of a more general theorem concerning the graphs
in space than one can formulate as follows:  That is to say N
points coloured in space.  Some of these points are dependent. 
Four points with more can be dependent two to two.  Two dependent
points are different colors.  Two nondependent points are of the
same color.  Two points of different colors are always dependent.
 Under these conditions four colors are enough to colour N points
of this graph.  Some mathematicians think that this general
theorem can be shown without computer, like his relationship to
the traditional theorem of the four colors.  See Bulletin
Association A.A.M.T.  N° 82 Août 2001. Email:

" Il faut parfois compliquer un problème pour en simplifier la
solution " ( Erdös )

Le théorème des quatre couleurs est un cas particulier d'un
théorème plus général concernant les graphes dans l'espace qu'on
peut formuler ainsi :

Soit N points colorés dans l'espace. Certains de ces points sont
liés. Quatre points au plus peuvent être liés deux à deux. Deux
points liés sont de couleurs différentes. Deux points non liés
sont de même couleur. Deux points de couleurs différentes sont
toujours liés.  Dans ces conditions quatre couleurs suffisent
pour colorer les N points de ce graphe.

Quelques mathématiciens pensent que ce théorème général peut être
démontré sans ordinateur, ainsi que sa relation avec le théorème
classique des quatre couleurs.

Voir Bulletin Association A.A.M.T. N° 82 Août 2001. Email:

4. Conferences:

Accepted paper for ISICT 06/2003 - Dublin, IR :

Accepted paper for SIAM Discrete Mathematics 08/2002 - San Diego CA : Details |

Rolland-Balzon Philippe