Abstrakt
A graph G is 5/2-critical if G has no circular 5/2-coloring (or equivalently, homomorphism to C (5)), but every proper subgraph of G has one. We prove that every 5/2-critical graph on n ae 4 vertices has at least edges, and list all 5/2-critical graphs achieving this bound.
This implies that every planar or projective-planar graph of girth at least 10 is 5/2-colorable.