D.B. West, Parameters of partial orders and graphs: packing, covering and representation. in Graphs and Orders (I. Rival ed.) D. Reidel Dordrecht (1985), 267-350. 10  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the maximal number of elements covered by a k antichain family. Since then several proofs of the cited results have been proposed [3] 5] 10] and [12] The Greene Kleitman theorem has been generalized to acyclic directed graphs in [11] 2] 1] and [13] An excellent survey is given by West [14]. The proof by Andr as Frank [5] is particularly elegant. Following Frank we call a chain family C and an antichain family A an orthogonal pair iff 1. P = i [ A2A A j [ i [ C2C C j , 2. jA Cj = 1 for all A 2 A; C 2 C. If C is obtained from C by adding the rest of P as singeltons ....

D.B. West, Parameters of partial orders and graphs: packing, covering and representation. in Graphs and Orders (I. Rival ed.) D. Reidel Dordrecht (1985), 267-350. 10

....(right) s s s s s s s s s s s s s s s s s s s s s s s s In this particular situation, the jump number of K is known to be one less than the difference between the number of edges in H( K) and the number of non extremal elements of K: s(K) 12 Gamma 4 Gamma 1 = 7. 7.2. Dimension We refer to [10, 23] for more details about dimension theory and an extensive list of references. Clearly, the dimension of any of the p kernels is at least 2 because they are not just chains. To decide whether the dimension exceeds 2, we must check the existence of an induced subordering belonging to the known list ....

D.B. West, Parameters of partial orders and graphs: Packing, covering, and representation, in I. Rival (ed.): Graphs and orders, D. Reidel Publishing Comp. (1985) 267-350.

....cf; dgg is neither a comparability nor an incomparability graph though the statement of the theorem holds. On the other hand, the graph G given by V = fa; b; c; d; e; fg ; E = fab; bc; ac; ad; be; cfg is perfect but the x i do not even form a partition. A general survey of the area was given in [9]. For generalizations to acyclic directed graphs, see [1] and the references therein. ....

D. B. West, Parameters of partial orders and graphs: Packing, covering and representation, in "Graphs and Orders" (I. Rival, Ed.), pp. 267-350, Reidel, Dordrecht, 1985.

....method to obtain a compact computer memory representation of orders and to compute pairwise comparisons efficiently. The principle of this method is to represent an order P as a union of interval orders P i for which an optimal representation is already known (i.e. a union representation of P [Wes85]) For a directed acyclic graph G = X; U) representing an order P = X; P ) the preprocessing time complexity is not better than the transitive closure computation cost. In the worst case, the size of the representation is the same that the size of the transitive closure. However, experimental ....

.... In this paper, we expose an original method for representing any order as a union of interval orders (where an interval order is a kind of order such that an optimal representation is known) Cap93] This kind of representation technique, called union representation, defined at first by West in [Wes85], has not been studied very much neither on theoretical, nor in practical point of view, which was a motivation for our work. In fact, it is an original approach of order representation. We present theoretical performance evaluation of our method and experimental comparison with the compression ....

Douglas B. West. Parameters of partial orders and graphs: packing, covering, and representation. In Ivan Rival, editor, Graphs and Orders, pages 267--350. NATO, D. Reidel publishing company, 1985.

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