{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:37Z","timestamp":1753893817638,"version":"3.41.2"},"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>The Shannon capacity of a graph $G$ is\u00a0$c(G)=\\sup_{d\\geq 1}(\\alpha(G^d))^{\\frac{1}{d}},$ where $\\alpha(G)$ is the independence number of $G$. The Shannon capacity of\u00a0the Kneser graph $\\mathrm{KG}_{n,r}$ was determined by Lov\u00e1sz\u00a0in 1979, but little is known about the Shannon capacity of the complement of that graph when $r$ does not divide $n$. The complement of the Kneser graph, $\\overline{\\mathrm{KG}}_{n,2}$, is also called the triangular graph $T_n$. The graph $T_n$ has the $n$-cycle $C_n$ as an induced subgraph, whereby $c(T_n) \\geq c(C_n)$, and these two families of graphs are closely related in the current context as both can be considered via geometric packings of the discrete $d$-dimensional torus of width $n$ using two types of $d$-dimensional cubes of width $2$. Bounds on $c(T_n)$ obtained in this work include $c(T_7) \\geq \\sqrt[3]{35} \\approx 3.271$, $c(T_{13}) \\geq \\sqrt[3]{248} \\approx 6.283$, $c(T_{15}) \\geq \\sqrt[4]{2802} \\approx 7.276$, and $c(T_{21}) \\geq \\sqrt[4]{11441} \\approx 10.342$.<\/jats:p>","DOI":"10.37236\/3214","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:12:47Z","timestamp":1578701567000},"source":"Crossref","is-referenced-by-count":2,"title":["On the Shannon Capacity of Triangular Graphs"],"prefix":"10.37236","volume":"20","author":[{"given":"Ashik Mathew","family":"Kizhakkepallathu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Patric RJ","family":"\u00d6sterg\u00e5rd","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexandru","family":"Popa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2013,5,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i2p27\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i2p27\/data","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i2p27\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T06:20:46Z","timestamp":1579242046000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i2p27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,9]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2013,4,9]]}},"URL":"https:\/\/doi.org\/10.37236\/3214","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,5,9]]},"article-number":"P27"}}