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

한국정보과학회 (Korean Institute of Information Scientists and Engineers)
권호 표지

재귀원형군의 일대일 서로소인 경로 커버

One-to-One Disjoint Path Covers in Recursive Circulants

  • 박정흠 (가톨릭대학교 컴퓨터정보공학부)
  • 발행 : 2003.12.01
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⟨ 이전 논문 다음 논문 ⟩

초록

이 논문에서는 주어진 두 정점 사이에 다른 모든 정점을 정확히 한번 지나는 k개의 서로소인 경로가 존재하는가 하는 일대일 서로소인 경로 커버 문제를 제안한다. 임의의 k, 임의의 두 정점 사이에 일대일 서로소인 경로 커버를 가지는 그래프는 해밀톤 연결되어 있다는 것보다 강한 해밀톤 성질을 가진다. 재귀원형군에서 이 문제를 고찰하여, 임의의$k(1{\leq}k{\leq}m)$에 대해서 $ G(2^m,4)$, $m{\geq}3$은 임의의 두 정점 사이에 k개의 경로로 이루어진 일대일 서로소인 경로 커버가 존재함을 보인다.

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.

키워드

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