39 research outputs found
Constrained Representations of Map Graphs and Half-Squares
The square of a graph H, denoted H^2, is obtained from H by adding new edges between two distinct vertices whenever their distance in H is two. The half-squares of a bipartite graph B=(X,Y,E_B) are the subgraphs of B^2 induced by the color classes X and Y, B^2[X] and B^2[Y]. For a given graph G=(V,E_G), if G=B^2[V] for some bipartite graph B=(V,W,E_B), then B is a representation of G and W is the set of points in B. If in addition B is planar, then G is also called a map graph and B is a witness of G [Chen, Grigni, Papadimitriou. Map graphs. J. ACM49 (2) (2002) 127-138].
While Chen, Grigni, Papadimitriou proved that any map graph G=(V,E_G) has a witness with at most 3|V|-6 points, we show that, given a map graph G and an integer k, deciding if G admits a witness with at most k points is NP-complete. As a by-product, we obtain NP-completeness of edge clique partition on planar graphs; until this present paper, the complexity status of edge clique partition for planar graphs was previously unknown.
We also consider half-squares of tree-convex bipartite graphs and prove the following complexity dichotomy: Given a graph G=(V,E_G) and an integer k, deciding if G=B^2[V] for some tree-convex bipartite graph B=(V,W,E_B) with |W|<=k points is NP-complete if G is non-chordal dually chordal and solvable in linear time otherwise. Our proof relies on a characterization of half-squares of tree-convex bipartite graphs, saying that these are precisely the chordal and dually chordal graphs
Graph Theory and Universal Grammar
Tese arquivada ao abrigo da Portaria nÂș 227/2017 de 25 de Julho-Registo de Grau EstrangeiroIn the last few years, Noam Chomsky (1994; 1995; 2000; 2001) has gone quite far in
the direction of simplifying syntax, including eliminating X-bar theory and the levels
of D-structure and S-structure entirely, as well as reducing movement rules to a
combination of the more primitive operations of Copy and Merge. What remain in
the Minimalist Program are the operations Merge and Agree and the levels of LF
(Logical Form) and PF (Phonological form).
My doctoral thesis attempts to offer an economical theory of syntactic structure
from a graph-theoretic point of view (cf. Diestel, 2005), with special emphases on the
elimination of category and projection labels and the Inclusiveness Condition
(Chomsky 1994). The major influences for the development of such a theory have
been Chris Collinsâ (2002) seminal paper âEliminating labelsâ, John Bowers (2001)
unpublished manuscript âSyntactic Relationsâ and the Cartographic Paradigm (see
Belletti, Cinque and Rizziâs volumes on OUP for a starting point regarding this
paradigm).
A syntactic structure will be regarded here as a graph consisting of the set of
lexical items, the set of relations among them and nothing more
Space and society : a study in socio-spatial dialectics with particular reference to Korean villages
Faculty Publications and Creative Works 1997
One of the ways we recognize our faculty at the University of New Mexico is through this annual publication which highlights our faculty\u27s scholarly and creative activities and achievements and serves as a compendium of UNM faculty efforts during the 1997 calendar year. Faculty Publications and Creative Works strives to illustrate the depth and breadth of research activities performed throughout our University\u27s laboratories, studios and classrooms. We believe that the communication of individual research is a significant method of sharing concepts and thoughts and ultimately inspiring the birth of new of ideas. In support of this, UNM faculty during 1997 produced over 2,770 works, including 2,398 scholarly papers and articles, 72 books, 63 book chapters, 82 reviews, 151 creative works and 4 patents. We are proud of the accomplishments of our faculty which are in part reflected in this book, which illustrates the diversity of intellectual pursuits in support of research and education at the University of New Mexico. Nasir Ahmed Interim Associate Provost for Research and Dean of Graduate Studie