{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:36Z","timestamp":1753893816959,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In our previous work, we introduced the random $k$-cut number for rooted graphs. In this paper, we show that the distribution of the $k$-cut number in complete binary trees of size n, after rescaling, is asymptotically a periodic function of $\\lg n \u2212 \\lg\u00a0\\lg n$. Thus there are different limit distributions for different subsequences, where these limits are similar to weakly $1$-stable distributions. This generalizes the result for the case $k = 1$, i.e., the traditional cutting model, by Janson (2004).<\/jats:p>","DOI":"10.37236\/8350","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T06:01:47Z","timestamp":1578636107000},"source":"Crossref","is-referenced-by-count":4,"title":["Cutting Resilient Networks \u2013 Complete Binary Trees"],"prefix":"10.37236","volume":"26","author":[{"given":"Xing Shi","family":"Cai","sequence":"first","affiliation":[]},{"given":"Cecilia","family":"Holmgren","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,12,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p43\/7970","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p43\/7970","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:01:07Z","timestamp":1579233667000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i4p43"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,6]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,10,11]]}},"URL":"https:\/\/doi.org\/10.37236\/8350","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,12,6]]},"article-number":"P4.43"}}