Prove that sub-trees have a common vertex
23008
For all $1 \leq i < j \leq k$, the subtrees $T_i$ and $T_j$ have a vertex in common. Show that $T$ has a vertex which is in all of the $T_i$.
116866
$A\times B$ connected component implies $A,B$ connect components
52261
Proof that any self-complementary graph has to have $4k$ or $4k+1$ vertex, for some $k \in \mathbb N$
59831
How to relate combinatorial proof to bipartite graphs?
113902
Show that there's a unique minimum spanning tree if all edges have different costs
148175
Girth and monochromatic copy of trees
136389
Finding an isomorphic subring of matrices
50886
Two disjoint spanning trees, spanning subgraph with all even degrees
39753
Proving that in a simple graph with $n$ vertices, two vertices have the same degree
7626
Proving that every connected graph has a vertex whose removal will not disconnect the graph.
158083
If $G$ is a connected graph with $n$ vertices and $n - 1$ edges then $G$ is a tree, using Induction.
89531
Show that every graph $G$ has a bipartite subgraph with at least half of the edges of $G$
142809
Trees whose complement is also a tree
50748
A pyramid $ABCDS$ in which all edges have different lengths and $|AS|+|CS|=|BS|+|DS|$
116538
Proof of Connected Diagrams
116932
Proving a simple graph is a connected graph
50417
Prove that the triangles $ABC$ and $AB^{'}C^{'}$ have the same incentre.