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

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

진구간 그래프의 서로소인 경로 커버에 대한 조건

Conditions for Disjoint Path Coverability in Proper Interval Graphs

  • 박정흠 (가톨릭대학교 컴퓨터정보공학부)
  • 발행 : 2007.10.15
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⟨ 이전 논문 다음 논문 ⟩

초록

이 논문에서는 진구간 그래프(proper interval graph)가 각각 일대일, 일대다. 다대다 k-서로소인 경로 커버를 가질 조건을 고찰한다. 진구간 그래프는 $k{\geq}2$인 경우, k-연결되어 있는 경우에만 일대일 k-서로소인 경로 커버를 가지며, k+1-연결되어 있는 경우에만 일대다 k-서로소인 경로 커버를 가짐을 증명하였다. 그리고 $k{\geq}3$일 때 진구간 그래프는 2k-1-연결되어 있는 경우에만 (쌍형) 다대다 k-서로소인 경로 커버를 가진다.

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.

키워드

참고문헌

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