Prove that there exists walks that each edge is in $G$
48184
Prove a graph Containing $2k$ odd vertices contains $k$ distinct trails
26449
$|G|=24$ prove that $G$ is not simple
145406
Prove every element of $G$ has finite order.
54516
Number of edges of any spanning tree of a graph $G$ coming from a subgraph of $G$
11003
Proving that $G/N$ is an abelian group
1453
Prove that the graph is connected
33822
Is there a monoid structure on the set of paths of a graph?
74961
Prove that every edge-coloring of $K_{17}$ with $3$ colors contains a monochromatic $K_3$.
113902
Show that there's a unique minimum spanning tree if all edges have different costs
93771
Prove that for any set $A$ there is some $x \notin A$
27366
Prove that $g$ is tangent to the graph of $f$
82578
Show that if $G$ is $2-$connected, then for any two vertices $u$ and $v$ there exists a cycle $C$ such that $u, v \in V (C)$
94928
Every $k$ vertices in an $k$ - connected graph are contained in a cycle.
151984
Proving the existence of a metric space
42389
If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$
129845
Prove that $T$ is a subgraph of $G$
123626
Prove that even $n$ can be partitioned to $\frac n2$ edges