Proving "A graph $G$ with chromatic number $𝑘$ has a proper coloring with a walk with $k$ vertices in $k$ different colors" by induction
41770
An $m$ coloured graph must have a path with each vertex taking up one colour each
27366
Prove that $g$ is tangent to the graph of $f$
59831
How to relate combinatorial proof to bipartite graphs?
142917
Graph vertex chromatic number in a union of 2 sub-graphs
72267
Prove there's a simple path of length $k$ in a simple graph $G$ where all the vertices have degree of at least $k$
139657
Prove that if $\chi(G-u-v)=\chi(G)-2$ for every vertices $u, v$ ($u \ne v$) then G is complete graph.
158856
Prove that a graph with the same number of edges and vertices contains one cycle
49703
Analogue of closed graph theorem
104349
Proof by induction involving symmetric groups
129845
Prove that $T$ is a subgraph of $G$
67887
Prove that a graph on $n$ vertices with girth $g$ has at most $\frac{g}{g-2}(n-2)$ edges
49879
A bipartite graph with a perfect matching has a vertex with each edge contained in a perfect matching
154038
A constructive lower bound on Ramsey numbers
6429
prove that a connected graph with $n$ vertices has at least $n-1$ edges
100256
Proof by induction on a rooted tree with even number of vertices
58481
Exclusion Inclusion Principle Induction Proof
28877
Graph with $k$ components.