Prove that if graph with $n$ vertices has at least $n$ edges, then graph has a cycle.
100978
If a graph with $n$ vertices and $n$ edges there must a cycle?
68638
Show that if $n\geq 3$, the complete graph on $n$ vertices $K_n$ contains a Hamiltonian cycle.
33216
Prove that the order of an element in $S_n$ equals the least common multiple of the lengths of the cycles in its cycle decomposition.
27373
Graph Proof by induction.
71170
Upper Bound on the Chromatic Number of a Graph with No Two Disjoint Odd Cycles
4112
How to prove that a simple graph having 11 or more vertices or its complement is not planar?
7626
Proving that every connected graph has a vertex whose removal will not disconnect the graph.
25382
Maximum number of edges in a bipartite graph
123626
Prove that even $n$ can be partitioned to $\frac n2$ edges
131736
Proving a triangle with different edge colors exists in a graph.
20544
Proving that if $G$ has a Hamiltonian circuit, then the line graph $L(G)$ also has a Hamiltonian Circuit
55944
Chromatic polynomial of connected graph $ \leq x(x-1)^{n-1}$
9847
Prove that if every node in a simple graph $G$ has degree $3$ or higher, then $G$ contains a cycle with a chord.
100168
Prove the existence of a graph of 15 vertices with some vertices degree given
100466
The number of labelled graphs with all vertices of even degree
1453
Prove that the graph is connected
115085
number of vertices in a self-complemntary graph