제한된 HL-그래프와 재귀원형군 $G(2^m,4)$에서 매칭 배제 문제

Matching Preclusion Problem in Restricted HL-graphs and Recursive Circulant $G(2^m,4)$

  • 박정흠 (가톨릭대학교 컴퓨터정보공학부)
  • 발행 : 2008.02.15

초록

그래프의 매칭 배제 집합은 그것을 삭제한 그래프가 완전 매칭이나 준완전 매칭을 가지지 않는 에지 집합이다. 매칭 배제수는 모든 매칭 배제 집합의 최소 크기이다. 이 논문에서는 임의의 $m{\geq}4$에 대하여 H-차원 제한된 HL-그래프와 재귀원형군 $G(2^m,4)$의 매칭 배제수는 분지수 m과 같고, 모든 최소 매칭 배제 집합은 한 정점에 인접한 에지 집합임을 보인다.

The matching preclusion set of a graph is a set of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. The matching preclusion number is the minimum cardinality over all matching preclusion sets. We show in this paper that, for any $m{\geq}4$, the matching preclusion numbers of both m-dimensional restricted HL-graph and recursive circulant $G(2^m,4)$ are equal to degree m of the networks, and that every minimum matching preclusion set is the set of edges incident to a single vertex.

키워드

참고문헌

  1. D.A. Reed and R.M. Fujimoto, Multicomputer Networks: Message-Based Parallel Processing, The MIT Press, 1987
  2. A.-H. Esfahanian, "Generalized measures of fault tolerance with application to n-cube networks," IEEE Trans. Computers 38(11), pp. 1586-1591, 1989 https://doi.org/10.1109/12.42131
  3. D. Kratsch, T. Kloks, and H. Muller, "Measuring the vulnerability for classes of intersection graphs," Discrete Applied Mathematics 77, pp. 259-270, 1997 https://doi.org/10.1016/S0166-218X(96)00133-3
  4. R.C. Brigham, F. Harary, E.C. Violin, J. Yellen, "Perfect-matching preclusion," Congressus Numerantium 174, pp. 185-192, 2005
  5. E. Cheng and L. Liptak, "Matching preclusion for some interconnection networks," Networks 50, pp. 173-180, 2007 https://doi.org/10.1002/net.20187
  6. J.-H. Park, H.-C. Kim, and H.-S. Lim, "Fault- hamiltonicity of hypercube-like interconnection networks," in Proc. of the IEEE International Parallel & Distributed Processing Symposium IPDPS 2005, Apr. 2005
  7. J.-H. Park and K.Y. Chwa, "Recursive circulants and their embeddings among hypercubes," Theoretical Computer Science 244, pp. 35-62, 2000 https://doi.org/10.1016/S0304-3975(00)00176-6
  8. J.-H. Park, H.-S. Lim, and H.-C. Kim, "Panconnectivity and pancyclicity of hypercube-like interconnection networks with faulty elements," Theoretical Computer Science 377, pp. 170-180, 2007 https://doi.org/10.1016/j.tcs.2007.02.029
  9. C.-H. Tsai, J.M. Tan, Y.-C. Chuang, and L.-H. Hsu, "Fault-free cycles and links in faulty recursive circulant graphs," in Proc. of Workshop on Algorithms and Theory of Computation ICS2000, pp. 74-77, 2000
  10. J.-H. Park, "Panconnectivity and edge-pancyclicity of faulty recursive circulant $G(2^m,4)$," Theoretical Computer Science, 390, pp. 70-80, 2008 https://doi.org/10.1016/j.tcs.2007.10.016