Journal of KIISE:Computer Systems and Theory (한국정보과학회논문지:시스템및이론)

Korean Institute of Information Scientists and Engineers (한국정보과학회)
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Many-to-Many Disjoint Path Covers in Double Loop Networks

이중 루프 네트워크의 다대다 서로소인 경로 커버

  • 박정흠 (카톨릭대학교 컴퓨터정보공학부)
  • Published : 2005.08.01
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Abstract

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.

그래프 G의 다대다 k-서로소인 경로 커버(k-DPC)는 k개의 서로 다른 소스 정점과 싱크 정점 쌍을 연결하며 그래프에 있는 모든 정점을 지나는 k개의 서로소인 경로 집합을 말한다. 이 논문에서는 이중 루프 네트워크 G(mn;1,m)에서 다대다 2-DPC를 고찰하여, 이분 그래프가 아닌 모든 G(mn;l,m), $m{\geq}3$은 임의의 두 소스-싱크 쌍을 연결하는 다대다 2-DPC가 존재하고 이분 그래프인 G(mn;1,m)은 두 흰색-검정 소스-싱크 쌍이거나 혹은 검정-검정, 흰색-흰색 쌍을 연결하는 2-DPC가 존재함을 보인다. G(mn;1,m)은 m이 홀수이고 n이 짝수일 경우에만 이분 그래프이다.

Keywords

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