{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:03Z","timestamp":1753893843363,"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>Let $n,k,b$ be integers with $1 \\le k-1 \\le b \\le n$ and let $G_{n,k,b}$ be the graph whose vertices are the $k$-element subsets $X$ of $\\{0,\\dots,n\\}$ with $\\mathrm{max}(X)-\\mathrm{min}(X) \\le b$ and where two such vertices $X,Y$ are joined by an edge if $\\mathrm{max}(X \\cup Y) - \\mathrm{min}(X \\cup Y) \\le b$. These graphs are generated by applying a transformation to maximal $k$-uniform hypergraphs of bandwidth $b$ that is used to reduce the (weak) edge clique covering problem to a vertex clique covering problem. The bandwidth of $G_{n,k,b}$ is thus the largest possible bandwidth of any transformed $k$-uniform hypergraph of bandwidth $b$. For $b\\geq \\frac{n+k-1}{2}$, the exact bandwidth of these graphs is determined. Moreover, the bandwidth is determined asymptotically for $b=o(n)$ and for $b$ growing linearly in $n$ with a factor $\\beta \\in (0,1]$, where for one case only bounds could be found. It is conjectured that the upper bound of this open case is the right asymptotic value.<\/jats:p>","DOI":"10.37236\/6900","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T14:50:01Z","timestamp":1578667801000},"source":"Crossref","is-referenced-by-count":0,"title":["Bandwidth of Graphs Resulting from the Edge Clique Covering Problem"],"prefix":"10.37236","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9396-5332","authenticated-orcid":false,"given":"Konrad","family":"Engel","sequence":"first","affiliation":[]},{"given":"Sebastian","family":"Hanisch","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,12,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p49\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p49\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:20:32Z","timestamp":1579234832000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i4p49"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,21]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,10,5]]}},"URL":"https:\/\/doi.org\/10.37236\/6900","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,12,21]]},"article-number":"P4.49"}}