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

Korean Institute of Information Scientists and Engineers (한국정보과학회)
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Paired Many-to-Many Disjoint Path Covers in Recursive Circulants and Tori

재귀원형군과 토러스에서 쌍형 다대다 서로소인 경로 커버

  • 김유상 (가톨릭대학교 컴퓨터공학과) ;
  • 박정흠 (가톨릭대학교 컴퓨터공학과)
  • Published : 2009.02.15
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Abstract

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 $f+2k{\leq}{\delta}-1$.

그래프 G의 쌍형 다대다 k-서로소인 경로 커버(쌍형 k-DPC)는 k개의 서로 다른 소스-싱크 쌍을 연결하며 그래프에 있는 모든 정점을 지나는 k개의 서로소인 경로 집합이다. 이 논문에서는 재귀원형군 G($cd^m$,d), $d{\geq}3$과 토러스에서 서로소인 경로 커버를 고려하여, 이분 그래프가 아니고 분지수가 $\delta$인 재귀원형군과 토러스는 고장 요소(정점이나 에지)가 f개 이하일 때 $f+2k{\leq}{\delta}-1$을 만족하는 임의의 f, $k{\geq}1$에 대하여 쌍형 k-DPC를 가짐을 보인다.

Keywords

References

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