Question

Anyone know any interesting open graph theory problems, unsolved problems that we could possibly write a paper on

Answer 1

I got chu

Answer 2

i want to see this O.O

Answer 3

Give me y = mx + b nub

Answer 4

lol

Answer 5

-.-

Answer 6

stupid cats

Answer 7

Dan is mad cuz he forgot teh basics

Answer 8

are you referring to Paul Erd˝os theories or no?

Answer 9

how about this
Is it true that every k-connected (k>1) graph which does not have a Hamiltonian cycle has a cycle that contains k independent vertices and their neighbors? This is known to be true for k = 2 and 3. For example, the graph to the right is 3-connected but not Hamiltonian. And the dotted cycle shown contains 3 independent vertices (the three vertices which are lighter in color) and thier neighbors. To see that it is not Hamiltonian, notice that this graph is just the complete bipartite graph K(3,4).

Answer 10

that is a nice one :)

Answer 11

what does it mean independent vertices and their neighbors

Answer 12

they exist on the same plane

Answer 13

get it?

Answer 14

not really a bit confused still

Answer 15

what does it mean 3-connected

Answer 16

my favorite is Euler trail but it already had a solution so :-\

Answer 17

vertices act as vertices. 3- means it has 3 independent vertices

Answer 18

lol its just kinnda intuitive

Answer 19

yea.. have fun i did this a while back and i really don't feel like doing it again but i had it saved so yea

Answer 20

ohh i see now

Answer 21

yea

Answer 22

cool

Answer 23

interesting.. so this thm says a cycle must exist such that it contains all the set of k independant vertices?