Showing papers by "Rolf H. Möhring published in 1994"
TL;DR: In this article, it was shown that the pathwidth of a cocomparability graph G equals its treewidth, based on a new notion, called interval width, for a partial orderP, which is the smallest width of an interval order contained in P, and which is shown to be equal to the trewidth of G.
Abstract: We show that the pathwidth of a cocomparability graphG equals its treewidth. The proof is based on a new notion, calledinterval width, for a partial orderP, which is the smallest width of an interval order contained inP, and which is shown to be equal to the treewidth of its cocomparability graph. We observe also that determining any of these parameters isNP-hard and we establish some connections between classical dimension notions of partial orders and interval width. In fact we develop approximation algorithms for interval width ofP whose performance ratios depend on the dimension and interval dimension ofP, respectively.
43 citations
TL;DR: This paper investigates a transformation P -> Q between partial orders P, Q that transforms the interval dimension of P to the dimension of Q, i.e., idim (P) = dim (Q), and turns out to be invariant with respect to changes of P that do not alter its comparability graph, thus also providing a simple new proof for the comparability invariance of interval dimension.
Abstract: This paper investigates a transformation P -> Q between partial orders P, Q that transforms the interval dimension of P to the dimension of Q, i.e., idim (P) = dim (Q). Such a construction has been shown before in the context of Ferrer's dimension by Cogis [Discrete Math., 38 (1982), pp. 47-52 ]. The construction in this paper can be shown to be equivalent to his, but it has the advantage of (1) being purely order-theoretic, (2) providing a geometric interpretation of interval dimension similar to that of Ore [Amer. Math. Soc. Colloq. Publ., Vol. 38, 1962] for dimension, and (3) revealing several somewhat surprising connections to other order-theoretic results. For instance, the transformation P -> Q can be seen as almost an inverse of the well-known split operation; it provides a theoretical background for the influence of edge subdivision on dimension (e.g., the results of Spinrad [Order, 5 (1989), pp. 143-147]) and interval dimension, and it turns out to be invariant with respect to changes of P that do not alter its comparability graph, thus also providing a simple new proof for the comparability invariance of interval dimension.
21 citations