Let $G(V,E)$ be an un-directed, un-connected graph. Prove that $\bar G$ is connected, And its Diameter is at most $2$.
69358
Given a simple graph and its complement, prove that either of them is always connected.
116932
Proving a simple graph is a connected graph
72267
Prove there's a simple path of length $k$ in a simple graph $G$ where all the vertices have degree of at least $k$
116538
Proof of Connected Diagrams
35458
Prove, that graph $G$ has at least $\chi(G)(\chi(G)-1)/2$ edges.
42367
Prove that simple graph $G$ is orientable
112731
If $Y$ is connected, why is $A\cup Y$ connected in this case?
97630
A graph which is not a single block has at least two leaf blocks
4602
Outline of a proof that $\mathbb{R}^2 - A$ where A is countable is path-connected
27253
Path connectedness of the set $\{(x,y):(x+1)^{2}+y^{2}\leq 1\}\cup\{(x,y):y=x\sin(\frac{1}{x}),x>0\}$
64993
Connectedness of the $S^2$ sphere
78110
A connected k-regular bipartite graph is 2-connected.
39455
Prove that $(X\times Y)\setminus (A\times B)$ is connected
5132
Given $A\cap \overline{B}\neq \emptyset$, prove $A\cup B$ connected.
38466
Proving that the number of vertices of odd degree in any graph G is even
63442
Show that if $U$ is an open connected subspace of $\mathbb{R}^2$, then $U$ is path connected
102084
How to show path-connectedness of $GL(n,\mathbb{C})$