A nowhere-zero k-tension on a graph G is a mapping from the edges of G to the set {±1, ±2,..., ±(k -1)} ⊂ ℤ such that, in any fixed orientation of G, for each circuit C the sum of the labels over the edges of C oriented in one direction equals the sum of values of the edges of C oriented oppositely. We show that the existence of an integral tension polynomial that counts nowherezero k-tension on a graph, due to Kochol, is a consequence of a general theory of inside-out polytopes. The same holds for tensions on signed graphs. We develop the...
