Mario Stefanutti
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 Jan25 asked Question about 3-regular graphs with a restriction (also fullerene and four color theorem) Nov17 answered Restrictions on the faces of a $3$-regular planar graph Nov17 revised Help with distribution and disposition of faces in a map (four color theorem) added 5 characters in body 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 accepted Four color theorem, 3-regular planar graph, Hamiltonian path and spiral chains 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? Jun15 asked Four color theorem, 3-regular planar graph, Hamiltonian path and spiral chains May30 answered Can the borders of a map be deformed to give arbitrary area to any region? Mar17 accepted How many different four coloring exist for a given regular map? Mar16 accepted Left or right edge in cubic planar graph 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 asked Left or right edge in cubic planar graph 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 awarded Commentator