Prove that every triangle-free graph is $\lceil 2\sqrt{n}\rceil$ colorable
90747
Upper bound on $\chi(G)$ for a triangle-free graph
9847
Prove that if every node in a simple graph $G$ has degree $3$ or higher, then $G$ contains a cycle with a chord.
158856
Prove that a graph with the same number of edges and vertices contains one cycle
7626
Proving that every connected graph has a vertex whose removal will not disconnect the graph.
61340
Prove that there exists bipartite graph with this degree sequence: $(3,3,3,3,3,5,6,6,6,6,6,6,6,6)$
140444
Prove $\chi(G)\chi(\bar{G}) \geq n$ for chromatic number of graph and its complement
138226
Finding All n-regular graphs on m vertices
117992
Help with graph induction proof
39753
Proving that in a simple graph with $n$ vertices, two vertices have the same degree
74730
Combinatorial Proof of ${{n}\choose{k}} {{k}\choose{j}} = {{n}\choose{j}} {{n-j}\choose{k-j}}$
38700
the Nordhaus-Gaddum problems for chromatic number of graph and its complement
24477
Monochromatic squares in a colored plane
83872
Isomorphisms for graphs with loops and multiple edges
68561
How to show $\lceil ( \sqrt3 +1)^{2n}\rceil$ where $n \in \mathbb{ N}$ is divisible by $2^{n+1}$
28877
Graph with $k$ components.
145718
Proving that A connected graph on $n$ vertices is a tree iff it has $n-1$ edges
7062
Can the complete graph $K_9$, be 2-coloured with no blue $K_4$ or red triangles?