{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T13:47:46Z","timestamp":1648993666672},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2012,3,6]],"date-time":"2012-03-06T00:00:00Z","timestamp":1330992000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Theory Comput Syst"],"published-print":{"date-parts":[[2013,2]]},"DOI":"10.1007\/s00224-012-9387-2","type":"journal-article","created":{"date-parts":[[2012,3,5]],"date-time":"2012-03-05T21:14:44Z","timestamp":1330982084000},"page":"303-318","source":"Crossref","is-referenced-by-count":1,"title":["On Reversible Cascades in Scale-Free and Erd\u0151s-R\u00e9nyi Random Graphs"],"prefix":"10.1007","volume":"52","author":[{"given":"Ching-Lueh","family":"Chang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chao-Hong","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,3,6]]},"reference":[{"issue":"44\u201346","key":"9387_CR1","doi-asserted-by":"crossref","first-page":"4017","DOI":"10.1016\/j.tcs.2010.08.021","volume":"411","author":"E. Ackerman","year":"2010","unstructured":"Ackerman, E., Ben-Zwi, O., Wolfovitz, G.: Combinatorial model and bounds for target set selection. Theor. Comput. Sci. 411(44\u201346), 4017\u20134022 (2010)","journal-title":"Theor. Comput. Sci."},{"key":"9387_CR2","unstructured":"Adams, S.S., Brass, Z., Stokes, C., Troxell, D.S.: Irreversible k-threshold and majority conversion processes on complete multipartite graphs and graph products. Technical Report arXiv:1102.5361 , Cornell University (2011)"},{"issue":"11","key":"9387_CR3","doi-asserted-by":"crossref","first-page":"4049","DOI":"10.1016\/j.camwa.2011.09.047","volume":"62","author":"S.S. Adams","year":"2011","unstructured":"Adams, S.S., Troxell, D.S., Zinnen, S.L.: Dynamic monopolies and feedback vertex sets in hexagonal grids. Comput. Math. Appl. 62(11), 4049\u20134057 (2011)","journal-title":"Comput. Math. Appl."},{"issue":"3\u20134","key":"9387_CR4","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1002\/(SICI)1098-2418(199810\/12)13:3\/4<409::AID-RSA11>3.0.CO;2-U","volume":"13","author":"J. Balogh","year":"1998","unstructured":"Balogh, J., Pete, G.: Random disease on the square grid. Random Struct. Algorithms 13(3\u20134), 409\u2013422 (1998)","journal-title":"Random Struct. Algorithms"},{"issue":"2","key":"9387_CR5","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1006\/jctb.2001.2045","volume":"83","author":"E. Berger","year":"2001","unstructured":"Berger, E.: Dynamic monopolies of constant size. J. Comb. Theory, Ser. B 83(2), 191\u2013200 (2001)","journal-title":"J. Comb. Theory, Ser. B"},{"issue":"3","key":"9387_CR6","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1016\/S0166-218X(02)00241-X","volume":"127","author":"J.-C. Bermond","year":"2003","unstructured":"Bermond, J.-C., Bond, J., Peleg, D., Perennes, S.: The power of small coalitions in graphs. Discrete Appl. Math. 127(3), 399\u2013414 (2003)","journal-title":"Discrete Appl. Math."},{"issue":"3","key":"9387_CR7","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1006\/game.1993.1023","volume":"5","author":"L.E. Blume","year":"1993","unstructured":"Blume, L.E.: The statistical mechanics of strategic interaction. Games Econ. Behav. 5(3), 387\u2013424 (1993)","journal-title":"Games Econ. Behav."},{"key":"9387_CR8","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511814068","volume-title":"Random Graphs","author":"B. Bollob\u00e1s","year":"2001","unstructured":"Bollob\u00e1s, B.: Random Graphs, 2nd edn. Cambridge University Press, Cambridge (2001)","edition":"2"},{"issue":"1","key":"9387_CR9","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s00493-004-0002-2","volume":"24","author":"B. Bollob\u00e1s","year":"2004","unstructured":"Bollob\u00e1s, B., Riordan, O.: The diameter of a scale-free random graph. Combinatorica 24(1), 5\u201334 (2004)","journal-title":"Combinatorica"},{"key":"9387_CR10","first-page":"159","volume-title":"Proceedings of the 1st Workshop on Combinatorial and Algorithmic Aspects of Networking","author":"A. Bonato","year":"2004","unstructured":"Bonato, A.: A survey of models of the Web graph. In: L\u00f3pez-Ortiz, A., Hamel, A. (eds.) Proceedings of the 1st Workshop on Combinatorial and Algorithmic Aspects of Networking, pp.\u00a0159\u2013172. Springer, Berlin, Heidelberg (2004)"},{"issue":"27\u201329","key":"9387_CR11","doi-asserted-by":"crossref","first-page":"2714","DOI":"10.1016\/j.tcs.2009.03.032","volume":"410","author":"C.-L. Chang","year":"2009","unstructured":"Chang, C.-L., Lyuu, Y.-D.: Spreading messages. Theor. Comput. Sci. 410(27\u201329), 2714\u20132724 (2009)","journal-title":"Theor. Comput. Sci."},{"key":"9387_CR12","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/978-3-642-13073-1_11","volume-title":"Proceedings of the 7th International Conference on Algorithms and Complexity","author":"C.-L. Chang","year":"2010","unstructured":"Chang, C.-L., Lyuu, Y.-D.: Bounding the number of tolerable faults in majority-based systems. In: Calamoneri, T., D\u00edaz, J. (eds.) Proceedings of the 7th International Conference on Algorithms and Complexity, Rome, Italy, pp.\u00a0109\u2013119. Springer, Berlin, Heidelberg (2010)"},{"issue":"2","key":"9387_CR13","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/s00224-010-9258-7","volume":"48","author":"C.-L. Chang","year":"2011","unstructured":"Chang, C.-L., Lyuu, Y.-D.: Spreading of messages in random graphs. Theory Comput. Syst. 48(2), 389\u2013401 (2011)","journal-title":"Theory Comput. Syst."},{"key":"9387_CR14","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1007\/978-3-642-25011-8_8","volume-title":"Proceedings of the 22nd International Workshop on Combinatorial Algorithms","author":"C.-L. Chang","year":"2011","unstructured":"Chang, C.-L., Lyuu, Y.-D.: Stable sets of threshold-based cascades on the Erd\u0151s-R\u00e9nyi random graphs. In: Proceedings of the 22nd International Workshop on Combinatorial Algorithms, pp.\u00a096\u2013105 (2011)"},{"issue":"1","key":"9387_CR15","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1080\/15427951.2004.10129081","volume":"1","author":"F. Chung","year":"2004","unstructured":"Chung, F., Lu, L.: The average distance in a random graph with given expected degrees. Internet Math. 1(1), 91\u2013114 (2004)","journal-title":"Internet Math."},{"key":"9387_CR16","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/978-3-540-44485-5_4","volume-title":"Complex Networks","author":"F. Chung","year":"2004","unstructured":"Chung, F., Lu, L.: The small world phenomenon in hybrid power law graphs. In: Ben-Naim, E., Frauenfelder, H., Toroczkai, Z. (eds.) Complex Networks, pp.\u00a089\u2013104. Springer, Berlin, Heidelberg (2004)"},{"issue":"5","key":"9387_CR17","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.90.058701","volume":"90","author":"R. Cohen","year":"2003","unstructured":"Cohen, R., Havlin, S.: Scale-free networks are ultrasmall. Phys. Rev. Lett. 90(5), 058701 (2003)","journal-title":"Phys. Rev. Lett."},{"issue":"6","key":"9387_CR18","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1109\/MCSE.2004.73","volume":"6","author":"D. Donato","year":"2004","unstructured":"Donato, D., Laura, L., Leonardi, S., Millozzi, S.: Simulating the Webgraph: A comparative analysis of models. Comput. Sci. Eng. 6(6), 84\u201389 (2004)","journal-title":"Comput. Sci. Eng."},{"issue":"7","key":"9387_CR19","doi-asserted-by":"crossref","first-page":"1615","DOI":"10.1016\/j.dam.2008.09.012","volume":"157","author":"P.A. Dreyer","year":"2009","unstructured":"Dreyer, P.A., Roberts, F.S.: Irreversible k-threshold processes: Graph-theoretical threshold models of the spread of disease and of opinion. Discrete Appl. Math. 157(7), 1615\u20131627 (2009)","journal-title":"Discrete Appl. Math."},{"issue":"5","key":"9387_CR20","doi-asserted-by":"crossref","first-page":"1047","DOI":"10.2307\/2951493","volume":"61","author":"G. Ellison","year":"1993","unstructured":"Ellison, G.: Learning, local interaction, and coordination. Econometrica 61(5), 1047\u20131071 (1993)","journal-title":"Econometrica"},{"issue":"1","key":"9387_CR21","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/S0166-218X(00)00388-7","volume":"113","author":"P. Flocchini","year":"2001","unstructured":"Flocchini, P., Geurts, F., Santoro, N.: Optimal irreversible dynamos in chordal rings. Discrete Appl. Math. 113(1), 23\u201342 (2001)","journal-title":"Discrete Appl. Math."},{"issue":"2","key":"9387_CR22","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/S1570-8667(03)00022-4","volume":"1","author":"P. Flocchini","year":"2003","unstructured":"Flocchini, P., Kr\u00e1lovi\u010d, R., Ru\u017ei\u010dka, P., Roncato, A., Santoro, N.: On time versus size for monotone dynamic monopolies in regular topologies. J. Discrete Algorithms 1(2), 129\u2013150 (2003)","journal-title":"J. Discrete Algorithms"},{"issue":"2","key":"9387_CR23","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/S0166-218X(03)00261-0","volume":"137","author":"P. Flocchini","year":"2004","unstructured":"Flocchini, P., Lodi, E., Luccio, F., Pagli, L., Santoro, N.: Dynamic monopolies in tori. Discrete Appl. Math. 137(2), 197\u2013212 (2004)","journal-title":"Discrete Appl. Math."},{"issue":"6","key":"9387_CR24","doi-asserted-by":"crossref","first-page":"1420","DOI":"10.1086\/226707","volume":"83","author":"M. Granovetter","year":"1978","unstructured":"Granovetter, M.: Threshold models of collective behavior. Am. J. Sociol. 83(6), 1420\u20131443 (1978)","journal-title":"Am. J. Sociol."},{"key":"9387_CR25","volume-title":"Algorithmic Game Theory","author":"J. Kleinberg","year":"2007","unstructured":"Kleinberg, J.: Cascading behavior in networks: Algorithmic and economic issues. In: Nisan, N., Roughgarden, T., Tardos, \u00c9., Vazirani, V. (eds.) Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)"},{"key":"9387_CR26","unstructured":"Kyn\u010dl, J., Lidick\u00fd, B., Vysko\u010dil, T.: Irreversible 2-conversion set is NP-complete. Technical Report KAM-DIMATIA Series 2009-933, Department of Applied Mathematics, Charles University, Prague, Czech Republic (2009)"},{"key":"9387_CR27","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1109\/ISTCS.1993.253475","volume-title":"Proceedings of the 2nd Israel Symposium on Theory of Computing Systems","author":"N. Linial","year":"1993","unstructured":"Linial, N., Peleg, D., Rabinovich, Y., Saks, M.: Sphere packing and local majorities in graphs. In: Proceedings of the 2nd Israel Symposium on Theory of Computing Systems, pp.\u00a0141\u2013149 (1993)"},{"issue":"2","key":"9387_CR28","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/S0020-0190(98)00039-8","volume":"66","author":"F. Luccio","year":"1998","unstructured":"Luccio, F.: Almost exact minimum feedback vertex set in meshes and butterflies. Inf. Process. Lett. 66(2), 59\u201364 (1998)","journal-title":"Inf. Process. Lett."},{"key":"9387_CR29","first-page":"204","volume-title":"Proceedings of the 6th International Colloquium on Structural Information & Communication Complexity","author":"F. Luccio","year":"1999","unstructured":"Luccio, F., Pagli, L., Sanossian, H.: Irreversible dynamos in butterflies. In: Proceedings of the 6th International Colloquium on Structural Information & Communication Complexity, pp.\u00a0204\u2013218 (1999)"},{"key":"9387_CR30","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1109\/FOCS.2009.64","volume-title":"Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science","author":"A. Montanari","year":"2009","unstructured":"Montanari, A., Saberi, A.: Convergence to equilibrium in local interaction games. In: Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science, pp.\u00a0303\u2013312 (2009)"},{"issue":"1","key":"9387_CR31","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1111\/1467-937X.00121","volume":"67","author":"S. Morris","year":"2000","unstructured":"Morris, S.: Contagion. Rev. Econ. Stud. 67(1), 57\u201378 (2000)","journal-title":"Rev. Econ. Stud."},{"key":"9387_CR32","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511814075","volume-title":"Randomized Algorithms","author":"R. Motwani","year":"1995","unstructured":"Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press, Cambridge (1995)"},{"key":"9387_CR33","unstructured":"Peleg, D.: Graph immunity against local influence. Technical Report CS96-11, Weizmann Science Press of Israel (1996)"},{"issue":"2\u20133","key":"9387_CR34","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/S0166-218X(98)00043-2","volume":"86","author":"D. Peleg","year":"1998","unstructured":"Peleg, D.: Size bounds for dynamic monopolies. Discrete Appl. Math. 86(2\u20133), 263\u2013273 (1998)","journal-title":"Discrete Appl. Math."},{"issue":"2","key":"9387_CR35","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/S0304-3975(01)00055-X","volume":"282","author":"D. Peleg","year":"2002","unstructured":"Peleg, D.: Local majorities, coalitions and monopolies in graphs: A review. Theor. Comput. Sci. 282(2), 231\u2013257 (2002)","journal-title":"Theor. Comput. Sci."},{"issue":"3","key":"9387_CR36","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1137\/S089548010444016X","volume":"19","author":"D.A. Pike","year":"2005","unstructured":"Pike, D.A., Zou, Y.: Decycling Cartesian products of two cycles. SIAM J. Discrete Math. 19(3), 651\u2013663 (2005)","journal-title":"SIAM J. Discrete Math."},{"issue":"9","key":"9387_CR37","doi-asserted-by":"crossref","first-page":"5766","DOI":"10.1073\/pnas.082090499","volume":"99","author":"D.J. Watts","year":"2002","unstructured":"Watts, D.J.: A simple model of global cascades on random networks. Proc. Natl. Acad. Sci. 99(9), 5766\u20135771 (2002)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"9387_CR38","volume-title":"Introduction to Graph Theory","author":"D.B. West","year":"2001","unstructured":"West, D.B.: Introduction to Graph Theory, 2nd edn. Prentice-Hall, New York (2001)","edition":"2"},{"key":"9387_CR39","series-title":"Proceedings Volume in the Santa Fe Institute Studies in the Sciences of Complexity","first-page":"267","volume-title":"Economy as an Evolving Complex System","author":"H.P. Young","year":"2006","unstructured":"Young, H.P.: The diffusion of innovations in social networks. In: Blume, L.E., Durlauf, S.N. (eds.) Economy as an Evolving Complex System. Proceedings Volume in the Santa Fe Institute Studies in the Sciences of Complexity, vol.\u00a03, pp.\u00a0267\u2013282. Oxford University Press, New York (2006)"}],"container-title":["Theory of Computing Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00224-012-9387-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00224-012-9387-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00224-012-9387-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T11:54:23Z","timestamp":1558698863000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00224-012-9387-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3,6]]},"references-count":39,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2013,2]]}},"alternative-id":["9387"],"URL":"https:\/\/doi.org\/10.1007\/s00224-012-9387-2","relation":{},"ISSN":["1432-4350","1433-0490"],"issn-type":[{"value":"1432-4350","type":"print"},{"value":"1433-0490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3,6]]}}}