prove if in connected graph degree of vertices is at most $d$ and there is one vertex of degree $d - 1$, then it can be colored in $d$ colors.
131031
Q: Proving G is d-colorable
116932
Proving a simple graph is a connected graph
57930
Chromatic polynomial properties
157939
prove that a graph is one-ended
49703
Analogue of closed graph theorem
126428
Prove the edges of a multigraph may be oriented such that the net-degree of any vertex is $\leq 1$.
52056
Chromatic Triangles on a $K_{17}$ graph
49193
Constructing a graph from a degree sequence
99746
Vertex cover in a graph with maximum degree of 3 and average degree of 2.
157150
Is the maximum degree of a planar graph 5?
72267
Prove there's a simple path of length $k$ in a simple graph $G$ where all the vertices have degree of at least $k$
59247
How many connected graphs over V vertices and E edges?
17868
How to calculate the number of possible connected simple graphs with $n$ labelled vertices
7626
Proving that every connected graph has a vertex whose removal will not disconnect the graph.
110760
Chromatic Polynomial
94838
Show that a self-complementary graph contains an odd number of vertices with degree $(n-1)/2$
41770
An $m$ coloured graph must have a path with each vertex taking up one colour each