Prove that if $\chi(G) > k \wedge |\{\operatorname{ad}(H): \text{$H$ is an induced subgraph of $G$}\}|$ then $G$ has a $k-regular$ induced subgraph?
51002
Regular graph (Homework)
49527
Prove that $a$ commutes with each of its conjugates in $G$ iff $a$ belongs to an abelian normal subgroup of $G$.
79367
Understanding the difference between two theorems related to $|G\,:\,K|=|H\,:\,K|\cdot|G\,:\,H|$.
35800
If $K \leq H \leq G$, show that $[G:K] = [G:H][H:K]$.
79730
$G$ is a planar, connected graph. Let $n$ be number of vertices, $m$ number of edges and $f$ number of faces. Prove that dual graph $G*$ has $f(G*)=n$
122330
Prove that there exists some $c\in(-3,3)$ such that$ \ \ g(c) \cdot g''(c)<0$.
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
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 $T_i$.
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
138410
Centralizer of $\mathbb{C}[G]$ in $\mathbb{C}[H]$
46863
Show that $g$ is injective
78379
Proof on cubic residues
94507
Given $G$ group and $H \le G$ such that $|G:H|=2$, how does $x^2 \in H$ for every $x \in G$?
131212
Prove that if $A$ is regular then $\operatorname{adj}(\operatorname{adj}(A)) = (\det A)^{n-2} A$
24147
$AG,AF$ are perpendiculars to the internal bisectors $CG,BF$ and $GF$ extended intersects $AB,AC$ at $H,I$
18540
Isomorphism from $\mathbb{C}[G]$ to $\prod_{i=1}^h M_{n_i}(\mathbb{C})$.
38785
Prove previsibility and $E[X_{T \wedge n}] \le E[X_{S \wedge n}]$