Vertex colorings of graphs without short odd cycles

An equitable coloring of a graph is a proper vertex coloring such that the sizes of every two color classes differ by at most 1. Chen, Lih, and Wu conjectured that every connected graph G with maximum degree @D>=2 has an equitable coloring with @D ...

A k -colouring of a graph G =( V , E ) is a mapping c : V {1,2, , k } such that c ( u ) c ( v ) whenever uv is an edge. The reconfiguration graph of the k -colourings of G contains as its vertex set the k -colourings of G , and two ...

A graph G is equitably k-choosable if, for any k-uniform list assignment L, G is L-colorable and each color appears on at most @?|V(G)|k@? vertices. A graph G is equitably k-colorable if G has a proper k-vertex coloring such that the sizes of any two ...