{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T14:45:53Z","timestamp":1754145953688,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Nordhaus and Gaddum proved sharp upper and lower bounds on the sum and product of the chromatic number of a graph and its complement. Over the years, similar inequalities have been shown for a plenitude of different graph invariants. In this paper, we consider such inequalities for the number of cliques (complete subgraphs) in a graph $G$, denoted $k(G)$. We note that some such inequalities have been well-studied, e.g., lower bounds on $k(G)+k(\\overline{G})=k(G)+i(G)$, where $i(G)$ is the number of independent subsets of $G$, has been come to be known as the study of Ramsey multiplicity. We give a history of such problems. One could consider fixed sized versions of these problems as well. We also investigate multicolor versions of these problems, meaning we $r$-color the edges of $K_n$ yielding graphs $G_1,G_2,\\ldots,G_r$ and give bounds on $\\sum k(G_i)$ and $\\prod k(G_i)$.<\/jats:p>","DOI":"10.37236\/13158","type":"journal-article","created":{"date-parts":[[2025,7,17]],"date-time":"2025-07-17T17:15:32Z","timestamp":1752772532000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Number of Monochromatic Cliques in a Graph"],"prefix":"10.37236","volume":"32","author":[{"given":"Deepak","family":"Bal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jonathan","family":"Cutler","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luke","family":"Pebody","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2025,7,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i3p16\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i3p16\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,17]],"date-time":"2025-07-17T17:15:32Z","timestamp":1752772532000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i3p16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,18]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,7,4]]}},"URL":"https:\/\/doi.org\/10.37236\/13158","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,18]]},"article-number":"P3.16"}}