If $G$ is a graph with at least one cut-vertex, then at least $2$ of the blocks of $G$ contain exactly $1$ cut-vertex
97630
A graph which is not a single block has at least two leaf blocks
47478
Show that any cyclic group of even order has exactly one element of order $2$
120617
No cycle containing edges $e$ and $g$ implies there is a vertex $u$ so that every path sharing one end with $e$ and another with $g$ contains $u$
75461
If $n>m$, then the number of $m$-cycles in $S_n$ is given by $\frac{n(n-1)(n-2)\cdots(n-m+1)}{m}$.
102539
Min. number of vertices in graph as function of $\kappa(G)$ and $\operatorname{diam}(G)$
128034
Problem on Extremal Graphs: three independent paths
39753
Proving that in a simple graph with $n$ vertices, two vertices have the same degree
78110
A connected k-regular bipartite graph is 2-connected.
51349
Minimal cut edges number in connected Eulerian graph.
49045
Graph theory: Tree holds two sub-tree with an amount of vertices
38466
Proving that the number of vertices of odd degree in any graph G is even
94928
Every $k$ vertices in an $k$ - connected graph are contained in a cycle.
93304
How to prove Graph with $n$ vertices has Edge Chromatic Number no more than $n/2$ edges
2900
How many $3$-subsets of $\{1,2,\ldots,10\}$ contain at least one even and one odd integer?
44304
Number of labeled trees which have one vertex of degree 4
67887
Prove that a graph on $n$ vertices with girth $g$ has at most $\frac{g}{g-2}(n-2)$ edges
129845
Prove that $T$ is a subgraph of $G$