Unsolved Problems

If a graph is the union of $n$ cliques of size $n$, no two of which share more than one vertex, then the chromatic number is $n$....

If $n$ complete graphs, each with $n$ vertices, have the property that every pair of complete graphs shares at most one vertex, can the entire graph b...

Can every tiling of $\mathbb{R}^n$ by unit hypercubes have two cubes that share a complete $(n-1)$-dimensional face?...

Is the chromatic number of a graph at most its clique cover number times the maximum chromatic number of its neighborhoods?...

Is the number of sum-free subsets of $\{1, 2, \ldots, n\}$ equal to $O(2^{n/2})$?...