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MT =84hyp {5,4} 16 no e 0.5:0:0 v 1:0:0" has a very beautyful
color graph! 16 no color graph
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EN-GB">MT =84hyp {5,4} 16 no e 0.5:0:0 v 1:0:0" has a very beautyful color =
graph! q/groups/10714925/tn/1867620670/name/color+graph+16no.jpg">16 no color grap=
h
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On 6/4/2012 8:26 PM, Roice Nelson wrote:
>
>
> I like how you laid out the graph, and how it emphasizes the special
> role of the white face :) It'd also be cool to see a presentation of
> the graph without intersections. That should be possible (embedded in
> 3D), though I guess it wouldn't be as nicely symmetrical as the one
> you made.
Any graph can be embedded in R3 without crossings. I believe that this
one can't be embedded in R2 without crossings.
>
> I searched around a little (on Google, Wikipedia, and Wolfram Alpha)
> to see if there was a special name for this graph, or for the graph
> you get after removing the red nodes, but did not have any luck. An
> interesting close call to the latter was the Grotzsch graph
>
How does one search for a graph? That sounds super-useful!
>
> For this tiling/coloring, we have 16 faces, 30 edges, and 15 vertices,
> giving a Euler Characteristic of 1 (projective plane). Seems like a
> lot of the asymmetrical colorings end up producing that topology.
What an interesting observation, Roice!
-Melinda
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On 6/4/2012 8:26 PM, Roice Nelson wrote:
com"
type=3D"cite">
special role of the white face=A0:)=A0 It'd also be cool to see a
presentation of the graph without intersections.=A0 That should be
possible (embedded in 3D), though I guess it wouldn't be as
nicely symmetrical as the one you made.
Any graph can be embedded in R3 without crossings. I believe that
this one can't be embedded in R2 without crossings.
com"
type=3D"cite">
Alpha) to see if there was a special name for this graph, or for
the graph you get after removing the red nodes, but did not have
any luck. =A0An interesting close call to the latter was the
href=3D"http://en.wikipedia.org/wiki/Gr%C3%B6tzsch_graph"
target=3D"_blank">Grotzsch graph.
How does one search for a graph? That sounds super-useful!
com"
type=3D"cite">
vertices, giving a Euler Characteristic of 1 (projective
plane).=A0 Seems like a lot of the asymmetrical colorings end up
producing that topology.
What an interesting observation, Roice!
-Melinda
com"
type=3D"cite">
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---2027350018-1969622098-1338872473=:22454
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Hello everyone. I recently joined the MC4D group and it was suggested to me=
to introduce myself and tell a little bit=A0about myself.
=A0
My name is Jacob.=A0I'm 17 years old and will turn 18 a few days after the =
Presidential elections. I have lived in Kenova, West Virginia my entire lif=
e, though I have visited=A014 other=A0states that I have been old enough to=
remember.=A0I have multiple interests, especially learning how to=A0progra=
m software and playing music. I'm not very experienced yet with programming=
other than on my TI-84, but I have played musical instruments since I=A0st=
arted with the trumpet in=A02004, and I=A0now can play 12 instruments in to=
tal. I hope to learn a woodwind at some point, preferably tenor sax. Despit=
e my musical tallent, I am not good at any other type of art. Frankly, I'm =
proud that I can draw a recognizable stick figure.=A0My hobbies include vid=
eogaming, speed cubing (didn't see that coming, did you), and playing guita=
r and singing=A0with my close=A0friend and drummer=A0in our metal / screamo=
=A0band temporarily named=A0Umbros... at least, it would be a band if there=
were
more permanent=A0members than just the two of us.
=A0
I may not be the most active member of most discusions, but feel free to em=
ail me any time, even just to chat.
Get your facts first, then you can distort them as you please.
-Mark Twain
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>
> Any graph can be embedded in R3 without crossings. I believe that this one
> can't be embedded in R2 without crossings.
>
ah, I hadn't considered making that general statement, but it makes perfect
sense. I think you're right about this one not being a planar
graph
since it lives on the projective plane.
For R3 embeddings of graphs, here's something interesting that is
reminiscent of crossings. There are some graphs that must have linked
cycles when embedded. An example is the Peterson
graph
which is the graph of a hemi-dodecahedron. No matter how you embed it, at
least two of the pentagonal faces will be linked.
> How does one search for a graph? That sounds super-useful!
>
Wolfram Alpha has an ever increasing library of graphs. Ed Pegg, Jr. of
mathpuzzle.com told me he and others are constantly extending that
database. You can search for things like "graph on 11
vertices
and that query currently has over 500 results, names and pictures, etc. I
can't seem to search for graphs with a particular number of vertices and
edges though, which seems like a big limitation (maybe there is a way).
Googling things like "graph with 11 vertices and 20 edges" can be helpful
as well, when you're initially trying to find your way around. In the
past, those kinds of searches have led me to collections like this
one
.
I wouldn't be surprised if there are queryable databases of graphs out
there. If anyone knows of such a thing, please do share.
seeya,
Roice
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der-left-style:solid" class=3D"gmail_quote">
Any graph can be embedded in R3 without crossings. I believe that
this one can't be embedded in R2 without crossings.
at general statement, but it makes perfect sense.=A0 I think you're rig=
ht about=A0this one=A0not being a lanar_graph">planar graph, since it lives on the projective plane.>
sting that is reminiscent of crossings.=A0 There are some graphs that must =
have linked cycles when embedded.=A0 An example is the .wikipedia.org/wiki/Petersen_graph">Peterson graph, which is the graph =
of a hemi-dodecahedron.=A0 No matter how you embed it, at least two of the =
pentagonal faces will be linked.adding-left:1ex;border-left-color:rgb(204,204,204);border-left-width:1px;bo=
rder-left-style:solid" class=3D"gmail_quote">
ful!
has an ever increasing library of graphs.=A0 Ed Pegg, Jr. of tp://mathpuzzle.com">mathpuzzle.com=A0told me he and others are constan=
tly extending that database.=A0 You can search for things like "f=3D"http://www.wolframalpha.com/input/?i=3Dgraph+on+11+vertices">graph on =
11 vertices", and that query currently has over 500 results, names=
and pictures, etc.=A0 I can't seem to search for graphs with a particu=
lar number of vertices and edges though, which seems like a big limitation =
(maybe there is a way).
20 edges" can be helpful as well, when you're initially trying to =
find your way around.=A0 In the past,=A0those kinds of searches have led me=
to collections like l">this one.
ases of graphs out there.=A0 If anyone knows of such a thing, please do sha=
re.
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