Let $n \ge 6$. Prove that it is not possible to partition the edges of $K_n$ into floor($\frac{n}{6}$) planar subgraphs.
43845
Partitioning the edges of $K_n$ into $\lfloor \frac n6 \rfloor$ planar subgraphs
73345
maximum size of a $k$-intersecting family of $[n]$
22977
How many $6$-integer subsets of $\{1, 2, 3, \ldots, 20\}$ have no consecutive integers?
118007
Not lifting your pen on the $n\times n$ grid
32754
Each number in a subset $S\subseteq \{1,\ldots,2n\}$ does not divide another one. Then $\max |S|$?
59780
how to show that when an edge is removed from K5, the resluting subgraph is planar.
155926
Prove there are k consecutive non-squarefree integers
90329
Prove there is no simple group of order $729$
26449
$|G|=24$ prove that $G$ is not simple
71935
Let $k$ be a natural number . Then $3k+1$ , $4k+1$ and $6k+1$ cannot all be square numbers.
56092
What is complexity of this max-edge subgraph problem?
62996
A problem regarding the proof of ${p^nk\choose p^n}\equiv k\mod p$, where $p\nmid k$.
137322
Construction of a triangle-free graph of chromatic number $1526$
55752
Prove that $n+1$ vectors in $\mathbb{R}^n$ cannot be linearly independent
72213
Can a $N-1$ rectifiable set be partitioned into countably many connected pieces?
48692
A problem about the graph theory
46469
$n$ Lines in the Plane