{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:46:16Z","timestamp":1787319976977,"version":"build-2736575974"},"reference-count":50,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["NI 369\/13-2"],"award-info":[{"award-number":["NI 369\/13-2"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["NI 369\/13-2"],"award-info":[{"award-number":["NI 369\/13-2"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100011264","name":"FP7 People: Marie-Curie Actions","doi-asserted-by":"publisher","award":["631163.11"],"award-info":[{"award-number":["631163.11"]}],"id":[{"id":"10.13039\/100011264","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["551145\/14"],"award-info":[{"award-number":["551145\/14"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>The composition technique is a popular method for excluding polynomial-size problem kernels for NP-hard parameterized problems. We present a new technique exploiting triangle-based fractal structures for extending the range of applicability of compositions. Our technique makes it possible to prove new no-polynomial-kernel results for a number of problems dealing with length-bounded cuts. In particular, answering an open question of Golovach and Thilikos [ Discrete Optim., 8 (2011), pp. 77--86], we show that, unless ${NP}\\subseteq {{coNP}}\/{{poly}}$, the NP-hard Length-Bounded Edge-Cut (LBEC) problem (delete at most $k$ edges such that the resulting graph has no $s$-$t$ path of length shorter than $\\ell$) parameterized by the combination of $k$ and $\\ell$ has no polynomial-size problem kernel. Our framework applies to planar as well as directed variants of the basic problems and also applies to both edge and vertex-deletion problems. Along the way, we show that LBEC remains NP-hard on planar graphs, a result which we believe is interesting in its own right.<\/jats:p>","DOI":"10.1137\/16m1088740","type":"journal-article","created":{"date-parts":[[2018,3,20]],"date-time":"2018-03-20T16:08:52Z","timestamp":1521562132000},"page":"656-681","source":"Crossref","is-referenced-by-count":6,"title":["Fractals for Kernelization Lower Bounds"],"prefix":"10.1137","volume":"32","author":[{"given":"Till","family":"Fluschnik","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Danny","family":"Hermelin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andr\u00e9","family":"Nichterlein","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rolf","family":"Niedermeier","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,3,20]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"G. 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