• Journal of KIISE:Computer Systems and Theory
• /
• v.34 no.10
• /
• pp.539-554
• /
• 2007

In this Paper, we investigate conditions for proper interval graphs to have k-disjoint path covers of three types each: one-to-one, one-to-many, and many-to-many. It was proved that for $k{\geq}2$, a proper interval graph is one-to-one k-disjoint path coverable if and only if the graph is k-connected, and is one-to-many k-disjoint path coverable if and only if the graph is k+1-connected. For $k{\geq}3$, a Proper interval graph is (paired) many-to-many k-disjoint path coverable if and only if the graph is 2k-1-connected.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.21 no.11
• /
• pp.2103-2108
• /
• 2017

For n points $p_i$ on the m-dimensional plane $R^m$ and a fixed range r, consider a set $T_i$ containing points the distances from $p_i$ of which are less than or equal to r. In case m=1, $T_i$ is an interval on a line, it is a circle on a plane when m=2. For the vertices corresponding to the sets $T_i$, there is an edge between the vertices if the two sets intersect. Then this graph is called an intersection graph G. For m=1 G is called a proper interval graph and for m=2, it is called an unit disk graph. In this paper, we are concerned in the intersection graph G(r) when r changes. In particular, we consider the problem to find the minimum r such that G(r)is connected. For this problem, we propose an O(n) algorithm for the proper interval graph and an $O(n^2{\log}\;n)$ algorithm for the unit disk graph. For the dynamic environment in which the points on a line are added or deleted, we give an O(log n) algorithm for the problem.

• The korean journal of orthodontics
• /
• v.31 no.2 s.85
• /
• pp.159-172
• /
• 2001

Three dimensional analysis of malocclusion and craniofacial deformation is essential for the successful orthodontic treatment. But the orthodontists are not familiar with diagnosis and treatment plane based on lateral cephalometric analysis. Since orthodontists do not posses a sufficient knowledge in standard value of posteroanterior cephalometric anaysis and of clinical importance for transverse jaw growth. In this study male(n=130) and female(n=171) aged from 6 to 16 and diagnosed as Class I malocclusion were selected to analysis width of cranium, maxilla and mandible on the posteroanterior cephalogram. The changes as a function of chronologic age and cervical vertebrae maturity index(CVXI) were examined. The Proper regression model was selected by sex with polynominal regression models and method of variable selection. Mean of each measurements and 70% confidence interval of individual measurement according to age was assesed and a graphs were made. Results are as follows :1. All the measurements for the width are gradually incresed as increase in chronologic age and CVMI. From the total amount of change between age 6 and 16, there is a tendency that mandibular width is broader than maxillary width and the width of male is broader than female. 2. There is no statistically significant sexual difference in Mx-Mn difference, Mx-Mn width differential, Mx/Mn ratio according to age and CVMI. 3. Mean of each measurement and 70% confidence interval of individual measurement according to age and sex were assessed and graphs were made for maxillary width, mandibular width, Mx-Mn difference, Mx/Mn ratio. 4. The width of maxilla and mandible in Korean children are broader than Western children during growth period.