Proof of connected graph having n-1 edge minimum with n vertices
6429
prove that a connected graph with $n$ vertices has at least $n-1$ edges
27407
every planar graph can be expressed as a union of five edge-disjoint forests
150508
∗∗Prove that each graph with an even number of vertices has two vertices with an even number of common neighbors.
38466
Proving that the number of vertices of odd degree in any graph G is even
89531
Show that every graph $G$ has a bipartite subgraph with at least half of the edges of $G$
89452
Proof about Graph with no triangle
27661
The closed graph theorem in topology
59831
How to relate combinatorial proof to bipartite graphs?
124666
Hamiltonian and non-Hamiltonian connected graph using the same degree sequence
18117
Maximum number of edges in a simple graph?
90747
Upper bound on $\chi(G)$ for a triangle-free graph
138226
Finding All n-regular graphs on m vertices
33316
Show that if $G$ is simple a graph with $n$ vertices and 􏰈the number of edges $m>\binom{n-1}{2}$, then $G$ is connected.
96803
Hall's marriage theorem in bipartite graph
113902
Show that there's a unique minimum spanning tree if all edges have different costs
158856
Prove that a graph with the same number of edges and vertices contains one cycle
94928
Every $k$ vertices in an $k$ - connected graph are contained in a cycle.