360 reputation
28
bio website 4coloring.wordpress.com
location Rome, Italy
age 45
visits member for 3 years, 3 months
seen 14 hours ago

Nov
25
comment Help with distribution and disposition of faces in a map (four color theorem)
I am pretty sure the identity is: $$F_5=12+F_7+2F_8+\cdots$$ Why the ">"? About the simplified map with 13 faces, I verified manually (computer program) that it does not exist. I agree that 13 pentagons is not possible because it would lead to the identity to be 13 = 12. Any other face with more than 6 edges would not work either. If we try with an $F_7$, the equilibrium would bend on the right of the equality and we would need 13 faces of type $F_5$ to balance it. The only possible solutions is to have 12 faces of type $F_5$ + 1 face of type $F_6$ = 13 faces. But these maps do not exist.
Nov
24
asked Help with distribution and disposition of faces in a map (four color theorem)
Jun
1
awarded  Teacher
Jun
1
answered Publishing elementary proofs of theorems
May
30
revised Is value of $\pi = 4$?
added 358 characters in body
May
30
answered Is value of $\pi = 4$?
May
21
answered Interesting properties for numbers 1-20?
May
19
awarded  Scholar
May
19
accepted Circle packing representation of a given graph
May
19
revised Circle packing representation of a given graph
added 264 characters in body
May
17
awarded  Supporter
May
16
asked Circle packing representation of a given graph
Apr
13
awarded  Editor
Apr
13
revised How many different four coloring exist for a given regular map?
added 235 characters in body
Apr
7
comment How many different four coloring exist for a given regular map?
In other words, for example, for maps with hundreds of faces, once a map has been properly four colored, I don't want to count all other colorings that derive from subsequent exchanges of colors. My doubt is how many "different" (in the meaning I explained) coloring exist for a given map? Is there a study on this that can help me?
Apr
4
comment How many different four coloring exist for a given regular map?
For what I'm trying to analyze, K4 has to be regarded as having just one possible coloring. In your K4 example, after the graph has been colored, through subsequent exchanges of colors, each K4 copy can be converted to any other. See this picture: 4coloring.wordpress.com/plus/k4-and-different-four-colorings. In other words, since when coloring K4 vertexes, colors can be choosen arbitrarily, any four coloring is equivalent. For more complex maps swapping colors won't help. I'd like to understand how this is related to the shape of the map. I want to add this tool to my java application.
Apr
3
awarded  Student
Apr
3
asked How many different four coloring exist for a given regular map?