Proof - a vertex in a path has an even number of edges
126060
Proving that a Euler Circuit has a even degree for every vertex
137072
Number Of Distinct Paths In A Rectangular Grid
39753
Proving that in a simple graph with $n$ vertices, two vertices have the same degree
18117
Maximum number of edges in a simple graph?
49585
Proof a graph is bipartite if and only if it contains no odd cycles
23008
For all $1 \leq i < j \leq k$, the subtrees $T_i$ and $T_j$ have a vertex in common. Show that $T$ has a vertex which is in all of the $T_i$.
100466
The number of labelled graphs with all vertices of even degree
86271
Spanning Trees: Prove if $e_1$ is an edge in $X$ that isn't in $Y$, then there exists an edge ...
99781
Proof that any simple connected graph has at least 2 non-cut 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?
129845
Prove that $T$ is a subgraph of $G$
155090
A graph whose every odd cycle is a triangle is 4-colorable
145818
Edges on an even number of Hamilton cycles
155993
A closed path is made up of 11 line segments. Can one line, not containing a vertex of the path, intersect each of its segments?
72267
Prove there's a simple path of length $k$ in a simple graph $G$ where all the vertices have degree of at least $k$
102084
How to show path-connectedness of $GL(n,\mathbb{C})$
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.