Strong matching preclusion. (English) Zbl 1232.05186
Summary: The matching preclusion problem, introduced by R. C. Brigham, F. Harary, E. C. Violin and J. Yellen [“Perfect-matching preclusion”, Congr. Numerantium 174, 185–192 (2005; Zbl 1091.05057)], studies how to effectively make a graph have neither perfect matchings nor almost perfect matchings by deleting as small a number of edges as possible. Extending this concept, we consider a more general matching preclusion problem, called the strong matching preclusion, in which deletion of vertices is additionally permitted. We establish the strong matching preclusion number and all possible minimum strong matching preclusion sets for various classes of graphs.
MSC:
| 05C70 | Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) |
Citations:
Zbl 1091.05057References:
| [1] | Aldred, R. E.L.; Anstee, R. P.; Locke, S. C., Perfect matchings after vertex deletions, Discrete Mathematics, 307, 3048-3054 (2007) · Zbl 1126.05077 |
| [2] | Biggs, N. L.; Smith, D. H., On trivalent graphs, Bulletin of the London Mathematical Society, 3, 155-158 (1971) · Zbl 0217.02404 |
| [3] | Bondy, J. A.; Murty, U. S.R., Graph Theory (2008), Springer · Zbl 1134.05001 |
| [4] | Brigham, R. C.; Harary, F.; Violin, E. C.; Yellen, J., Perfect-matching preclusion, Congressus Numerantium, 174, 185-192 (2005) · Zbl 1091.05057 |
| [5] | Cheng, E.; Lesniak, L.; Lipman, M. J.; Lipták, L., Conditional matching preclusion sets, Information Sciences, 179, 8, 1092-1101 (2009) · Zbl 1221.05265 |
| [6] | Cheng, E.; Lipták, L.; Lipman, M. J.; Toeniskoetter, M., Conditional matching preclusion for the alternating group graphs and split-stars, International Journal of Computer Mathematics, 88, 6, 1120-1136 (2011) · Zbl 1210.05107 |
| [7] | Cheng, E.; Lipták, L., Matching preclusion for some interconnection networks, Networks, 50, 2, 173-180 (2007) · Zbl 1123.05073 |
| [8] | Choi, H.-A.; Nakajima, K.; Rim, C. S., Graph bipartization and via minimization, SIAM Journal on Discrete Mathematics, 2, 1, 38-47 (1989) · Zbl 0677.68036 |
| [9] | Guichard, D. R., Perfect matchings in pruned grid graphs, Discrete Mathematics, 308, 6552-6557 (2008) · Zbl 1214.05121 |
| [10] | Hsieh, S.-Y.; Lee, C.-W., Conditional edge-fault hamiltonicity of matching composition networks, IEEE Transactions on Parallel and Distributed Systems, 20, 4, 581-592 (2009) |
| [11] | Lai, P.-L.; Tan, J. J.M; Tsai, C.-H.; Hsu, L.-H., The diagnosability of the matching composition network under the comparison diagnosis model, IEEE Transactions on Computers, 53, 8, 1064-1069 (2004) |
| [12] | Park, J.-H., Matching preclusion problem in restricted HL-graphs and recursive circulant \(G(2^m, 4)\), Journal of KIISE, 35, 2, 60-65 (2008) |
| [13] | Park, J.-H.; Chwa, K. Y., Recursive circulants and their embeddings among hypercubes, Theoretical Computer Science, 244, 35-62 (2000) · Zbl 0945.68003 |
| [14] | J.-H. Park, H.-C. Kim, H.-S. Lim, Fault-hamiltonicity of hypercube-like interconnection networks, in: Proc. IEEE International Parallel and Distributed Processing Symposium IPDPS 2005, Denver, April 2005.; J.-H. Park, H.-C. Kim, H.-S. Lim, Fault-hamiltonicity of hypercube-like interconnection networks, in: Proc. IEEE International Parallel and Distributed Processing Symposium IPDPS 2005, Denver, April 2005. |
| [15] | Park, J.-H.; Kim, H.-C.; Lim, H.-S., Many-to-many disjoint path covers in the presence of faulty elements, IEEE Transactions on Computers, 58, 4, 528-540 (2009) · Zbl 1368.68090 |
| [16] | Park, J.-H.; Son, S. H., Conditional matching preclusion for hypercube-like interconnection networks, Theoretical Computer Science, 410, 27-29, 2632-2640 (2009) · Zbl 1172.68006 |
| [17] | C.-H. Tsai, J.J.M. Tan, Y.-C. Chuang, L.-H. Hsu, Fault-free cycles and links in faulty recursive circulant graphs, in: Proc. of the Workshop on Algorithms and Theory of Computation ICS 2000, 2000, pp. 74-77.; C.-H. Tsai, J.J.M. Tan, Y.-C. Chuang, L.-H. Hsu, Fault-free cycles and links in faulty recursive circulant graphs, in: Proc. of the Workshop on Algorithms and Theory of Computation ICS 2000, 2000, pp. 74-77. |
| [18] | A.S. Vaidya, P.S.N. Rao, S.R. Shankar, A class of hypercube-like networks, in: Proc. of the 5th IEEE Symposium on Parallel and Distributed Processing SPDP 1993, December 1993, pp. 800-803.; A.S. Vaidya, P.S.N. Rao, S.R. Shankar, A class of hypercube-like networks, in: Proc. of the 5th IEEE Symposium on Parallel and Distributed Processing SPDP 1993, December 1993, pp. 800-803. |
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