  We introduce a new graph invariant that measures fractional covering of a
graph by cuts. Besides being interesting in its own right, it is useful for
study of homomorphisms and tension-continuous mappings. We study the relations
with chromatic number, bipartite density, and other graph parameters.
  We find the value of our parameter for a family of graphs based on
hypercubes. These graphs play for our parameter the role that circular cliques
play for the circular chromatic number. The fact that the defined parameter
attains on these graphs the `correct' value suggests that the definition is a
natural one. In the proof we use the eigenvalue bound for maximum cut and a
recent result of Engstr\"om, F\"arnqvist, Jonsson, and Thapper.
  We also provide a polynomial time approximation algorithm based on
semidefinite programming and in particular on vector chromatic number (defined
by Karger, Motwani and Sudan [Approximate graph coloring by semidefinite
programming, J. ACM 45 (1998), no. 2, 246--265]).

Combinatorics