• 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.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 $f+2k{\leq}{\delta}-1$.

• Journal of KIISE:Computer Systems and Theory
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• v.28 no.8
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• pp.399-405
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• 2001

이 논문은 재귀원형군 G(2$^{m}$ , 2$^{k}$ )의 강한 해밀톤 성질을 그래프 이론적 관점에서 고찰한다. 재귀원형군은 [9]에서 제안된 다중 컴퓨터의 연결망 구조이다. G(2$^{m}$ , 2$^{k}$ )가 임의의 정점 쌍 ν, $\omega$를 잇는 길이 ι인 경로를 가지는가 하는 문제를 고려하여, (a) G(2$^{m}$ , 2$^{k}$ )는 ι$\geq$d(ν, $\omega$)을 만족하는 모든 ι에 대해서 길이 ι인 경로를 가지며, (b) G(2$^{m}$ , 4)는 ι$\geq$d(ν, $\omega$)+2인 모든 길이의 경로를 가지며, (c)G(2$^{m}$ , 2$^{k}$ ), k$\geq$3은 길이 d(ν, $\omega$)+2$^{k}$ -3인 경로를 가지지 않는 정점 쌍이 있음을 보인다. 여기서, d(ν, $\omega$)는 ν와 $\omega$ 사이의 거리이다.

• 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.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.