Let G be a simple planar graph on 13 vertices. Prove that at least one of G and its complement G is not planar.
67383
Prove that $G'$ is not planar.
123626
Prove that even $n$ can be partitioned to $\frac n2$ edges
72417
Bipartite graphs
154564
Prove that the sum of minimum edge cover and maximum matching is the vertex count
59780
how to show that when an edge is removed from K5, the resluting subgraph is planar.
139657
Prove that if $\chi(G-u-v)=\chi(G)-2$ for every vertices $u, v$ ($u \ne v$) then G is complete graph.
126428
Prove the edges of a multigraph may be oriented such that the net-degree of any vertex is $\leq 1$.
11329
Proving a graph has no Hamiltonian cycle
71170
Upper Bound on the Chromatic Number of a Graph with No Two Disjoint Odd Cycles
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.
43555
Show that a finite regular bipartite graph has a perfect matching
90256
Example of a simple graph isomorphic to a permutation group.
60076
A graph $G$ is bipartite if and only if $G$ can be coloured with 2 colours
117020
Regular $n$-gon in the plane with vertices on integers?
158856
Prove that a graph with the same number of edges and vertices contains one cycle
90747
Upper bound on $\chi(G)$ for a triangle-free graph
97515
Is this graph a planar graph or not?