Mario Stefanutti
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 Aug22 comment Find if it is possible to draw a closed (cycle; not a path) continuous line… I am not really sure to have understood the question, but if I did ... if you have two neighbours vertices with an odd number of edges it is impossible what you are asking. This is because if the path passes through a vertex walking on two of its edges the only way to pass also on the third one would be if that edge is the last one of the entire path. Moreover since you are looking for a cycle the same reasoning can be done with just one vertex Jan31 comment Help with distribution and disposition of faces in a map (four color theorem) The "far far away land" it is full also of F4 faces (squares) :-) Nice category of graphs, thanks! Jan25 comment Question about 3-regular graphs with a restriction (also fullerene and four color theorem) With 17 and 19 faces for sure fullerene exist: hog.grinvin.org/Fullerenes Jan25 comment Question about 3-regular graphs with a restriction (also fullerene and four color theorem) I did a quick check but for now the sequence 1,0,1,1,3 has 252 match. I suppose still too few elements! Nov17 comment Restrictions on the faces of a $3$-regular planar graph Hi I was analyzing something similar and I think these may interest you. Search ("Simplified maps of 13 faces do not exist!") whithin this page: 4coloring.wordpress.com/open-points-and-notes and read this other question: math.stackexchange.com/questions/158620/… Jun22 comment Four color theorem, 3-regular planar graph, Hamiltonian path and spiral chains @Daniel. I verified them with Mathematica and all those graphs are isomorphic! Jun19 comment Four color theorem, 3-regular planar graph, Hamiltonian path and spiral chains @Daniel. I'm verifying if all graphs (I have 10980 cases) are all isomorphic and, so far (I tried some random graphs), they all are. Let me check some other cases and I will accept your answer! But now that you made me notice that, it seems intuitive and I am pretty convinced they are. Thanks! Jun16 comment Four color theorem, 3-regular planar graph, Hamiltonian path and spiral chains @draks: Is the only graph with these characteristics a Dodecahedron? Jun16 comment Four color theorem, 3-regular planar graph, Hamiltonian path and spiral chains Hi, draks. Thanks for the answer, but can you help me to understand how does it relate to my question? Does it mean (imply) that all 3-regular graphs with 20 vertices have Hamiltonian paths? Jun15 comment Four color theorem, 3-regular planar graph, Hamiltonian path and spiral chains Some graphs I was talking about are in this video: youtube.com/watch?v=MyEn2B-hAag&feature=g-upl Jun15 comment Four color theorem, 3-regular planar graph, Hamiltonian path and spiral chains Yes, all these graphs have 20 vertices and 30 edges. One question about your answer. You wrote that "The 3-regular graph with these properties is the Dodecahedron". Yes, but that is just one of the possible graphs, right? Mar16 comment Left or right edge in cubic planar graph Your argument about mirroring the planar image of the graph convinced me. What a pity! I think I have to go the other way and elaborate the image by pattern recognition. In my case, since I have a particular kind of maps, it is not going to be so difficult. Thanks! Mar16 comment Left or right edge in cubic planar graph I am trying to identify some particular chains of a cubic planar graph (see 4coloring.wordpress.com/spiral-chains). To get these chains I was considering to convert the graph that I have into a graph theory model in memory (adjacency list) and then apply the algorithm to find the chain, but is it possible algorithmically to identify left and right edges? For example I know it is possible to use an algorithm to test planarity (en.wikipedia.org/wiki/Planarity_testing), but is it possible to do something similar to identify left and right edges? Mar16 comment How to find all proper colorings (four coloring) of a graph with a brute force algorithm Yes it does, but that is exactly why I'm looking for an algorithm. I'm working with graphs that have 30-50 vertices and that makes impossible to find all possible colorings and then filter them out. I'l like to write something similar to the function colorIt() inside this java code: - maps-coloring.git.sourceforge.net/git/… implementing for example a new method called findAllColorings() Mar15 comment How to find all proper colorings (four coloring) of a graph with a brute force algorithm How do I find all functions f:V→{1,2,3,4}? All possible functions, without filtering them first (for not valid coloring), seem to be a very high number of solutions. Mar15 comment How to find all proper colorings (four coloring) of a graph with a brute force algorithm Wow, how fast! I'll take a look into it. For my level it seems too difficult to understand and implement, but i'll try to see what I can do. I was hoping for a simpler approach to the problem! Thanks for the info Feb11 comment planar embedding a graph Draw your graph on the sphere. Your edge $e$ divides two faces. Choose one of these two faces. Now imagine the sphere made of very elastic rubben, make a small hole to the chosen face and blow into it. Enlarge the hole and flatten the balloon (the sphere) to adhere to the plane. The face you chosed is now the outer face of the graph. Dec3 comment Help with distribution and disposition of faces in a map (four color theorem) Do you know if there is an online version of this paper or an equivalent study on the subject? Nov25 comment Help with distribution and disposition of faces in a map (four color theorem) Thanks. I'll try to get a copy! Nov25 comment Help with distribution and disposition of faces in a map (four color theorem) I used a computer program I am building to create simplified maps (sourceforge.net/projects/maps-coloring). The program did not return any map of 13 faces. At the beginning I thought to a bug in the software, then I sketched a proof I thing is right (4coloring.wordpress.com/open-points-and-notes)