Distance graphs having large chromatic numbers and not containing   cliques or cycles of given size
  In this work, the classical Nelson -- Hadwiger problem is studied which lies on the edge of combinatorial geometry and graph theory. It concerns colorings of distance graphs in $ {\mathbb R}^n $, i.e., graphs such that their vertices are vectors and their edges are pairs of vectors at a distance from a given set of postive numbers apart. A series of new lower bounds are obtained for the chromatic numbers of such graphs with different restrictions on the clique numbers and the girths. 
Evgeniy Demekhin, Andrei Raigorodskii, Oleg Rubanov
math.CO