Conjecture A triangle-free graph with maximum degree has chromatic number at most .
For any simple digraph , we let be the number of unordered pairs of nonadjacent vertices (i.e. the number of non-edges), and be the size of the smallest feedback edge set.
Conjecture If is a simple digraph without directed cycles of length , then .
Problem Does every triangle-free planar graph of maximum degree three have circular chromatic number at most ?
Problem Does there exist a graph with no subgraph isomorphic to which cannot be expressed as a union of triangle free graphs?
Problem Is there an eighth triangle free strongly regular graph?