We show that every n-vertex planar graph admits a simultaneous embedding without mapping and with fixed edges with any (n/2)vertex planar graph. In order to achieve this result, we prove that every n-vertex plane graph has an induced outerplane subgraph containing at least n/2 vertices. Also, we show that every n-vertex planar graph and every n-vertex planar partial 3-tree admit a simultaneous ...

While attempting to classify partial linear spaces produced during the execution of an extension of Stinson’s hill-climbing algorithm a new problem arises, that of generating all graphical degree sequences that are diamond-free (i.e. have no diamond as subgraph) and satisfy additional constraints. We formalize this new problem, propose a constraint programming solution and list all satisfying d...

In this paper, we present a comparison of several important methods to solve fuzzy partial differential equations (PDEs). These include the reduced transform method (RDTM), Adomian decomposition (ADM), Homotopy perturbation (HPM), and analysis (HAM). A distinguishing practical feature these techniques is administered without need use discretion or restricted assumptions. Moreover, investigate (...

ÐWe propose a new measure of fuzzy equality comparison based on the similarity of possibility distributions. we define a type of fuzzy equi±join based on the new fuzzy equality comparison, and allow threshold values to be associated with predicates of the join condition. A sort±merge join algorithm based on a partial order of intervals is used to evaluate the fuzzy equi-join. In order for the e...

Since Lotfi A. Zadeh introduced the concept of fuzzy sets in 1965, many authors have devoted their efforts to the study of these new sets, both from a theoretical and applied point of view. Fuzzy sets were later extended in order to get more adequate and flexible models of inference processes, where uncertainty, imprecision or vagueness is present. Type 2 fuzzy sets comprise one of such extensi...

This paper is focused on an introduction of a new software product, which is called FuzzME. This software was developed as a tool for creating fuzzy models of multiple-criteria evaluation and decision making. The type of evaluations employed in the fuzzy models fully corresponds with the paradigm of the fuzzy set theory; the evaluations express the (fuzzy) degrees of fulfillment of correspondin...