Show that a graph with with exactly 1 vertex of degree 1, contains a cycle
49289
Need a counter example for cycle in a graph
28877
Graph with $k$ components.
37984
Prove a planar graph with all regions having even degree can be colored with 2 colors
94838
Show that a self-complementary graph contains an odd number of vertices with degree $(n-1)/2$
42367
Prove that simple graph $G$ is orientable
49585
Proof a graph is bipartite if and only if it contains no odd cycles
124666
Hamiltonian and non-Hamiltonian connected graph using the same degree sequence
100466
The number of labelled graphs with all vertices of even degree
110422
Prove that a graph $G$ is a forest if and only if every induced subgraph of $G$ contain a vertex of degree at most $1$
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.
46309
Prove that this graph is nonplanar
49879
A bipartite graph with a perfect matching has a vertex with each edge contained in a perfect matching
1453
Prove that the graph is connected
31626
proving that a graph is hamiltonian (Ore's theorem)
6429
prove that a connected graph with $n$ vertices has at least $n-1$ edges
127277
Graph Theory: Tree has at least 2 vertices of degree 1
75101
Let G = (V, E) be a simple undirected graph with n = |V | ≥ 1 vertices...