The purpose of this study is to evaluate the fitting accuracy and fracture resistance of crowns using a hybrid zirconia frame made of both porous and dense zirconia. Commercial semi-sintered zirconia, sintered dense zirconia and sintered hybrid zirconia were used. Sintered zirconia was milled using the CAD/CAM system, and semi-sintered zirconia was milled and sintered to fabricate molar crown f...

Properly colored cycles in edge-colored graphs are closely related to directed oriented graphs. As an analogy of the well-known Caccetta–Häggkvist Conjecture, we study existence properly bounded length graph. We first prove that for all integers s and t with ≥ 2 , every graph G no K contains a spanning subgraph H which admits orientation D such cycle is . Using this result, show r 4 if Conjectu...

The study of problems modeled by edge-colored graphs has given rise to important developments during the last few decades. For instance, the investigation of spanning trees for graphs provide important and interesting results both from a mathematical and an algorithmic point of view (see for instance [1]). From the point of view of applicability, problems arising in molecular biology are often ...

Abstract We consider maximum properly edge-colored trees in edge-colored graphs Gc. We also consider the problem where, given a vertex r, determine whether the graph has a spanning tree rooted at r, such that all root-to-leaf paths are properly colored. We consider these problems from graphtheoretic as well as algorithmic viewpoints. We prove their optimization versions to be NP-hard in general...

Let G be a planar graph with n vertices whose vertex set is partitioned into subsets V0, . . . , Vk−1 for some positive integer 1 ≤ k ≤ n and let S be a set of n distinct points in the plane partitioned into subsets S0, . . . , Sk−1 with |Vi| = |Si| (0 ≤ i ≤ k − 1). This paper studies the problem of computing a crossing-free drawing of G such that each vertex of Vi is mapped to a distinct point...