Unsolved Problems

Are there graphs on n vertices requiring more than floor(n/2) copies of each letter for word-representation?...

Classify graphs with representation number exactly 3....

Among bipartite graphs, do crown graphs require the longest word-representants?...

If every edge has imbalance ≥1, is the multiset of edge imbalances always graphic?...

Is the bondage number of a graph always ≤ 3Δ/2, where Δ is the maximum degree?...

Does there exist a perfect cuboid—a rectangular parallelepiped with integer edges, face diagonals, and space diagonal?...

Does every non-total finite poset have two elements x,y with P(x before y in random linear extension) ∈ [1/3, 2/3]?...

Do Lychrel numbers exist in base 10?...