Show that a graph $G$ is a forest if and only if every induced subgraph of $G$ contains a vertex of degree at most $1$
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 $1$
48692
A problem about the graph theory
126060
Proving that a Euler Circuit has a even degree for every vertex
60076
A graph $G$ is bipartite if and only if $G$ can be coloured with 2 colours
61340
Prove that there exists bipartite graph with this degree sequence: $(3,3,3,3,3,5,6,6,6,6,6,6,6,6)$
75101
Let G = (V, E) be a simple undirected graph with n = |V | ≥ 1 vertices...
13226
If $n$ is a natural number $\ge 2$ how do I prove that any graph with $n$ vertices has at least two vertices of the same degree?
72267
Prove there's a simple path of length $k$ in a simple graph $G$ where all the vertices have degree of at least $k$
131137
If ${\lvert{E(G)}\rvert}>{\lvert{V(G)}\rvert}+3$, graph $G$ has at least two disjoint cycles.
100466
The number of labelled graphs with all vertices of even degree
116932
Proving a simple graph is a connected graph
148376
Proving that a Binary Tree of $n$ nodes has a height of at least $\log(n)$.
6429
prove that a connected graph with $n$ vertices has at least $n-1$ edges
96620
Condition on degrees for existence of a tree
67887
Prove that a graph on $n$ vertices with girth $g$ has at most $\frac{g}{g-2}(n-2)$ edges
54516
Number of edges of any spanning tree of a graph $G$ coming from a subgraph of $G$
52261
Proof that any self-complementary graph has to have $4k$ or $4k+1$ vertex, for some $k \in \mathbb N$