Show that $K_n$ is not the union of two planar graphs
4112
How to prove that a simple graph having 11 or more vertices or its complement is not planar?
130751
Lower bound for monochromatic triangles in $K_n$
58329
Show that $y_1$ and $y_2$ are not Linearly Independent
70761
Number of ways to connect sets of $k$ dots in a perfect $n$-gon
89452
Proof about Graph with no triangle
43555
Show that a finite regular bipartite graph has a perfect matching
108417
Cycles of length k in a complete simple graph with n vertices
153550
Is there any connection between distributive lattices and planar graphs?
117992
Help with graph induction proof
67383
Prove that $G'$ is not planar.
42714
A diagram which is not the torus
123742
Proving connectedness of the $n$-sphere
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.
106801
Labelled spanning trees of $K_n-e$
96803
Hall's marriage theorem in bipartite graph
91777
Product of Non-Disjoint Cycles
31854
Proof - raising adjacency matrix to $n$-th power gives $n$-length walks between two vertices