{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T17:01:23Z","timestamp":1776963683676,"version":"3.51.4"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Liu, Hong, Gu, and Lai proved if the second largest eigenvalue of the adjacency matrix of graph $G$ with minimum degree $\\delta \\ge 2m+2 \\ge 4$ satisfies $\\lambda_2(G) &lt; \\delta - \\frac{2m+1}{\\delta+1}$, then $G$ contains at least $m+1$ edge-disjoint spanning trees, which verified a generalization of a conjecture by Cioab\u0103 and Wong. We show this bound is essentially the best possible by constructing $d$-regular graphs $\\mathcal{G}_{m,d}$ for all $d \\ge 2m+2 \\ge 4$ with at most $m$ edge-disjoint spanning trees and $\\lambda_2(\\mathcal{G}_{m,d}) &lt; d-\\frac{2m+1}{d+3}$. As a corollary, we show that a spectral inequality on graph rigidity by Cioab\u0103, Dewar, and Gu is essentially tight.<\/jats:p>","DOI":"10.37236\/10350","type":"journal-article","created":{"date-parts":[[2022,6,16]],"date-time":"2022-06-16T18:32:41Z","timestamp":1655404361000},"source":"Crossref","is-referenced-by-count":2,"title":["Extremal Graphs for a Spectral Inequality on Edge-Disjoint Spanning Trees"],"prefix":"10.37236","volume":"29","author":[{"given":"Sebastian M.","family":"Cioab\u0103","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anthony","family":"Ostuni","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Davin","family":"Park","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sriya","family":"Potluri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tanay","family":"Wakhare","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wiseley","family":"Wong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2022,6,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i2p56\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i2p56\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,16]],"date-time":"2022-06-16T18:32:41Z","timestamp":1655404361000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i2p56"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,17]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,4,8]]}},"URL":"https:\/\/doi.org\/10.37236\/10350","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,17]]},"article-number":"P2.56"}}