Proof that a $k$-regular bipartite graph has a $1$-factor
43555
Show that a finite regular bipartite graph has a perfect matching
103146
Proof that the Rubik’s Cube group is 2-generated
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
52261
Proof that any self-complementary graph has to have $4k$ or $4k+1$ vertex, for some $k \in \mathbb N$
106801
Labelled spanning trees of $K_n-e$
74730
Combinatorial Proof of ${{n}\choose{k}} {{k}\choose{j}} = {{n}\choose{j}} {{n-j}\choose{k-j}}$
153763
Prove that $a_1!\cdots a_k! < n!$ whenever $a_1+\cdots+a_k < n$
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
142534
Proof of $k {n\choose k} = n {n-1 \choose k-1}$ using direct proof
94639
Proof that the rank of a skew-symmetric matrix is at least $2$
101520
Let $G$ be a graph of minimum degree $k>1$. Show that $G$ has a cycle of length at least $k+1$
142861
Multipartite graphs which are not planar
94838
Show that a self-complementary graph contains an odd number of vertices with degree $(n-1)/2$
62996
A problem regarding the proof of ${p^nk\choose p^n}\equiv k\mod p$, where $p\nmid k$.
117685
Prove that a bipartite planar graph has a vertex of degree at most 3
72417
Bipartite graphs
48184
Prove a graph Containing $2k$ odd vertices contains $k$ distinct trails