• Proceedings of the Korean Information Science Society Conference
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• 2010.06b
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• pp.487-492
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• 2010

그래프에서 k-서로소인 경로 커버는 정점 집합을 커버하면서 정점이 서로소인 .개의 경로들의 집합으로 정의하고, 이때 각 경로는 주어진 소스와 싱크를 잇는다. 각 소스와 싱크에 요구(demand)라고 부르는 양의 정수가 주어질 때, 요구가 d인 각 소스나 싱크가 d개의 경로에 포함되는 일반-요구 k-서로소인 경로 커버(general-demand k-disjoint path cover)를 정의할 수 있다. 이것은 일대일, 일대다, 그리고 비쌍형 다대다 서로소인 경로 커버를 일반화한 것이다. 이 논문에서는 일반-요구 k-서로소인 경로 커버 문제가 비쌍형 k-서로소인 경로 커버 문제로 변환될 수 있음을 보인다. 더구나 소스가 하나인 경우를 단일-소스 k-서로소인 경로 커버(single-source k-disjoint path cover)라고 부르는데, 이것은 일대다 k-서로소인 경로 커버 문제로 변환된다.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.10
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• pp.539-554
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• 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 KIISE:Computer Systems and Theory
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• v.30 no.12
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• pp.691-698
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• 2003

In this paper, we propose a problem, called one-to-one disjoint path cover problem, whether or not there exist k disjoint paths joining a pair of vertices which pass through all the vertices other than the two exactly once. A graph which for an arbitrary k, has a one-to-one disjoint path cover between an arbitrary pair of vertices has a hamiltonian property stronger than hamiltonian-connectedness. We investigate this problem on recursive circulants and prove that for an arbitrary k $k(1{\leq}k{\leq}m)$$ G(2^m,4)$,$m{\geq}3$, has a one-to-one disjoint path cover consisting of k paths between an arbitrary pair of vortices.

• Journal of KIISE:Computer Systems and Theory
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• v.36 no.1
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• pp.40-51
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• 2009

A paired many-to-many k-disjoint path cover (paired k-DPC) of a graph G is a set of k disjoint paths joining k distinct source-sink pairs in which each vertex of G is covered by a path. In this paper, we investigate disjoint path covers in recursive circulants G($cd^m$,d) with $d{\geq}3$ and tori, and show that provided the number of faulty elements (vertices and/or edges) is f or less, every nonbipartite recursive circulant and torus of degree $\delta$ has a paired k-DPC for any f and $k{\geq}1$ with $f+2k{\leq}{\delta}-1$.

• Korean Journal of Plant Tissue Culture
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• v.28 no.6
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• pp.317-321
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• 2001

This study was carried out with Lilium oriental hybrid cv. Casa Blanca to observe the effect of in vitro culture conditions on ex vitro sprouting of bulblets. Low temperature (15$^{\circ}C$) inhibited the growth of in vitro bulblets while high temperature ($25^{\circ}C$) enhanced the growth. Bulblets cultured at 15$^{\circ}C$ did not show dormacy while those cultured at 2$0^{\circ}C$ ,$25^{\circ}C$ had a longer dormancy period. High sucrose concentration (9%) induced longer dormancy. Dormancy period was also prolonged in bulblets cultured in vitro at high temperature ($25^{\circ}C$). Dormancy period was more affected by in vitro culture temperature rather than sucrose concentration. Physiological dormancy was released more rapidly when bulblets were cultured at $25^{\circ}C$ for 6 weeks and further transferred at 15$^{\circ}C$ and cultured for another 12 weeks. Treatment of ABA induced the dormancy in Lilium bulblets but when bulblets were subjected to chilling treatment (4$^{\circ}C$ for 8 weeks) nearly 100% sprouting were observed. The medium containing 1.0 mg/L BA or 1.0 mg/L fluridone was also effective to produce non-dormant bulblets.

• Journal of KIISE:Computer Systems and Theory
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• v.33 no.10
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• pp.789-796
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• 2006

An unpaired many-to-many k-disjoint nth cover (k-DPC) of a graph G is a set of k disjoint paths joining k distinct sources and sinks in which each vertex of G is covered by a path. Here, a source can be freely matched to a sink. In this paper, we investigate unpaired many-to-many DPC's in a subclass of hpercube-like interconnection networks, called restricted HL-graphs, and show that every n-dimensional restricted HL-graph, $(m{\geq}3)$, with f or less faulty elements (vertices and/or edges) has an unpaired many-to-many k-DPC for any $f{\geq}0\;and\;k{\geq}1\;with\;f+k{\leq}m-2$.

• Journal of KIISE:Computer Systems and Theory
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• v.32 no.8
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• pp.426-431
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• 2005

A many-to-many k-disjoint path cover (k-DPC) of a graph G is a set of k disjoint paths joining k distinct source-sink pairs in which each vertex of G is covered by a path. In this paper, we investigate many-to-many 2-DPC in a double loop network G(mn;1,m), and show that every nonbipartite G(mn;1,m), $m{\geq}3$, has 2-DPC joining any two source-sink pairs of vertices and that every bipartite G(mn;1,m) has 2-DPC joining any two source-sink pairs of black-white vertices and joining any Pairs of black-black and white-white vertices. G(mn;l,m) is bipartite if and only if n is odd and n is even.

• FLOWER RESEARCH JOURNAL
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• v.16 no.3
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• pp.161-167
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• 2008

Eight species of Korean native lilies were used as plant materials and investigated for the effect of temperature, day length, and sucrose on enlargement of bulblet in vitro. enlargement of bulblet was enhanced at $25^{\circ}C$ in most of Korean native lilies tested, meanwhile it was promoted at $20^{\circ}C$ in L. davuricum and L. hansonii. Moreover, enlargement of bublet was promoted under dark in L. concolor var. parthneion, L. distichum, L. amabile, and L. davuricum, to the contrary fresh weight was increased under longer day length in L. hansonii and L. maximowitzii. That of L. concolor var. parthneion and L. cernuum was not affected by light or dark condition. Fresh weight of the bulblets produced in vitro of most Korean native lilies tested was increased with increasing sucrose concentration and best at $120g{\cdot}L^{-1}$ sucrose in medium. However, enlargement of bublet was promoted by $60g{\cdot}L^{-1}$ sucrose in L. tsingtauense and L. cernuum and by $90g{\cdot}L^{-1}$ in L. davuricum. Bulblet enlargement tended to promote by lower rate of scaly leaf occurrence or separating bulblet and it was affected by occurrence of scaly leaf rather than separation of bulblet. However, occurrence of scaly leaf, separation of bulblet, and enlargement of bulblet were more significantly affected by genetic factors, species rather than culture conditions.

• Proceedings of the Korean Information Science Society Conference
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• 2011.06b
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• pp.492-495
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• 2011

그래프 G의 쌍형 다대다 k-서로소민 경로 커버 (k-DPC)는 k개의 서로 다른 소스 정점과 싱크 정점 쌍을 연결하며 그래프에 있는 모든 정점을 지나는 k개의 서로소인 경로 집합을 말한다. 2-차원 $m{\times}n$ 토러스는 길이가 각각 m과 n인 두 사이클 $C_m$과 $C_n$의 곱으로 정의되는 그래프이다. 이 논문에서는 고장 정접이나 에지가 하나인 $m{\times}n$ 이분 토러스(짝수 m,n ${\geq}$4)에는, 정점 고장이 있고 소스나 싱크 중에 고장 정점과 같은 색을 가진 정점이 오직 하나 존재하거나 혹은 정점 고장이 없고 에지 고장이 하나 존재하면서 둘은 흰색 정점이고 둘은 검정색 정점이면 항상 두 소스-싱크 쌍을 잇는 쌍형 다대다 2-DPC가 존재 힘을 보인다.

• Proceedings of the Korean Information Science Society Conference
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• 2008.06a
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• pp.353-354
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• 2008