A simple combinatorial characterization of Markov sources which satisfy this condition is given in terms of cycles of the

underlying graph of the Markov chain.

While they are close in size, we observe that the cost of routing over the different graphs is different, and correlated to the

underlying graph structure.

It is NP-complete to decide whether an undirected graph G is the

underlying graph of an oriented clique.

1) is established on the linearity, it is in fact truly for the linear and non-liner cases because the

underlying graph of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]-flow can be decomposed into bouquets and dipoles, hold with conditions of Theorem 4.

SIGMA]) consists of an

underlying graph S together with a set of atomic constraints [C.

alpha]W), where A is the maximum degree of the

underlying graph of W.

n] = (G, [micro])), where G = (V, E) is a graph called the

underlying graph of [S.

A sigraph is an ordered pair S = (G, [sigma]), where G = (V,E) is a graph called

underlying graph of S and [sigma]: E [right arrow] {+, -} is a function.

1) Variations of the graph data structure: The choice of the

underlying graph data structure is affected by decisions on the abstract (mathematical) and on the technical level.

Without loss of generality, we assume that the

underlying graph is connected so that C(U, [bar]U) [is greater than] 0 for all U.

In our paper we showed that the

underlying graph theoretic model of hierarchical opposition is a twin binary tree in which the two 'son' nodes of every 'father' node have the same pair of contrastive labels: pure and impure in the Indian caste system, male and female in Indonesia, and land and noble in Fiji.

The parameter G in the definition of PQ tells LEDA that the

underlying graph is G.