MathCastle
Graph TheoryChallengeGraph Coloring

Graph Coloring · Challenge problem

The "book" graph BkB_k has two hub vertices joined by an edge, plus kk further "page" vertices each joined to BOTH hubs (2k+12k+1 edges on k+2k+2 vertices total). With 44 colors available, what is the smallest kk for which BkB_k has more than 10,00010{,}000 proper colorings?