41. It unifies the ideas of incidence chromatic number of a graph and game chromatic number in case of an undirected graph. 42. It unifies the ideas of incidence chromatic number of a graph and game chromatic number in case of an undirected graph. 43. Because there exist-clique-free graphs of arbitrarily large chromatic number , the Henson graphs have infinite chromatic number. 44. Because there exist-clique-free graphs of arbitrarily large chromatic number, the Henson graphs have infinite chromatic number . 45. A version of the conjecture that uses the fractional chromatic number in place of the chromatic number is known to be true. 46. A version of the conjecture that uses the fractional chromatic number in place of the chromatic number is known to be true. 47. The Balaban 10-cage has chromatic number 2, chromatic index 3, diameter 6, girth 10 and is hamiltonian. 48. It has independence number 52, chromatic number 3, chromatic index 3, radius 6, diameter 8 and girth 11. 49. The Horton graph has chromatic number 2, chromatic index 3, radius 10, diameter 10 and edge-connected graph. 50. An undirected graph is perfect if, in every induced subgraph, the chromatic number equals the size of the largest clique.
