Show that for any simple graph G one of G and G′ is connected.
69358
Given a simple graph and its complement, prove that either of them is always connected.
39753
Proving that in a simple graph with $n$ vertices, two vertices have the same degree
131137
If ${\lvert{E(G)}\rvert}>{\lvert{V(G)}\rvert}+3$, graph $G$ has at least two disjoint cycles.
45337
Suppose that $V, W$ are closed in $X$ and that $V\cap W, V\cup W$ are connected. Show that $V$ and $W$ are connected.
38466
Proving that the number of vertices of odd degree in any graph G is even
75101
Let G = (V, E) be a simple undirected graph with n = |V | ≥ 1 vertices...
84654
The graph of xy = 1 is connected or not
105666
What's an easy way to show that $GL(n,\mathbb C)$ is connected?
126428
Prove the edges of a multigraph may be oriented such that the net-degree of any vertex is $\leq 1$.
27373
Graph Proof by induction.
131736
Proving a triangle with different edge colors exists in a graph.
108417
Cycles of length k in a complete simple graph with n vertices
89452
Proof about Graph with no triangle
93304
How to prove Graph with $n$ vertices has Edge Chromatic Number no more than $n/2$ edges
93623
Showing that every connected open set in a locally path connected space is path connected
91253
Proving that every graph that each vertex at degree 2 must contain a cycle
70538
Intersection and union of simply connected domain