BACKGROUND AND AIM: Severe rotation of tooth is one of the most common problems in orthodontics and considered as a developmental phenomenon. These rotations can cause cosmetic problems, gingival recession, and traumatic occlusion. By using removable appliances, severe rotations can be treated. Furthermore, gingival damage, tooth attrition, and transposition of other teeth could be prevented. E...

Caccetta and Haggkvist 111 conjectured that every directed graph with n vertices and minimum outdegree k contains a (directed) cycle of length at most [n/k\. (T o see that this bound cannot be improved, consider the directed graph with n cyclically arranged vertices and with edges leading from each vertex u to the first k vertices following u in the cyclic order.) Our main result (Theorem 2) is...

A graph G 1⁄4 ðV ;EÞ is vertex-pancyclic if for every vertex u and any integer l ranging from a positive constant L to jV j, G contains a cycle C of length l such that u is in C. In this paper, we show that an n-dimensional augmented cube, where n P 2, is vertex-pancyclic with L 1⁄4 3. 2007 Elsevier Inc. All rights reserved.

A feedback vertex set of a graph is a subset of vertices containing at least one vertex from every cycle of the graph. Given a directed graph by its adjacency relation, we develop a relational algorithm for computing a feedback vertex set of minimum size. In combination with a BDD-implementation of relations, it allows to exactly solve this NP-hard problem for medium-sized graphs.

Let D be a directed graph of order n. An anti-directed Hamilton cycle H in D is a Hamilton cycle in the graph underlying D such that no pair of consecutive arcs in H form a directed path in D. We prove that if D is a directed graph with even order n and if the indegree and the outdegree of each vertex of D is at least 23n then D contains an anti-directed Hamilton cycle. This improves a bound of...

Let T be an edge weighted tree, let dT (u, v) be the sum of the weights of the edges on the path from u to v in T , and let dmin and dmax be two non-negative real numbers such that dmin ≤ dmax. Then a pairwise compatibility graph of T for dmin and dmax is a graph G = (V, E), where each vertex u ∈ V corresponds to a leaf u of T and there is an edge (u, v) ∈ E if and only if dmin ≤ dT (u, v) ≤ dm...

A split graph is a whose vertex set can be partitioned into clique and stable set. Given G weight function \(w: V(G) \rightarrow \mathbb {Q}_{\ge 0}\), the Split Vertex Deletion (SVD) problem asks to find minimum of vertices X such that \(G-X\) graph. It easy show if only it does not contain 4-cycle, 5-cycle, or two edge matching as an induced subgraph. Therefore, SVD admits 5-approximation alg...

distal extension removable partial denture is a prosthesis with lack of distal dental support with a 13-fold difference in resiliency between the mucosa and the periodontal ligament, resulting in leverage during compression forces. it may be potentially destructive to the abutments and the surrounding tissues. the aim of this study was to assess the effect of implant location on stress distribu...

Given an undirected and vertex weighted graph G, the Weighted Feedback Vertex Problem (WFVP) consists in finding a subset F ⊆ V of vertices of minimum weight such that each cycle in G contains at least one vertex in F . The WFVP on general graphs is known to be NP-hard. In this paper we introduce a new class of graphs, namely the diamond graphs, and give a linear time algorithm to