{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T04:36:31Z","timestamp":1776227791590,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $\\chi(G$) and $\\chi_f(G)$ denote the chromatic and fractional chromatic numbers of a graph $G$, and let $(n^+ , n^0 , n^-)$ denote the inertia of $G$. We prove that:\\[1 + \\max\\left(\\frac{n^+}{n^-} , \\frac{n^-}{n^+}\\right) \\le \\chi(G)\\] and conjecture that \\[ 1 + \\max\\left(\\frac{n^+}{n^-} , \\frac{n^-}{n^+}\\right) \\le \\chi_f(G).\\] We investigate extremal graphs for these bounds and demonstrate that this inertial bound is not a lower bound for the vector chromatic number. We conclude with a discussion of asymmetry between $n^+$ and $n^-$, including some Nordhaus-Gaddum bounds for inertia.<\/jats:p>","DOI":"10.37236\/6404","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:58:54Z","timestamp":1578671934000},"source":"Crossref","is-referenced-by-count":13,"title":["An Inertial Lower Bound for the Chromatic Number of a Graph"],"prefix":"10.37236","volume":"24","author":[{"given":"Clive","family":"Elphick","sequence":"first","affiliation":[]},{"given":"Pawel","family":"Wocjan","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,3,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p58\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p58\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:03:02Z","timestamp":1579237382000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i1p58"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,1,20]]}},"URL":"https:\/\/doi.org\/10.37236\/6404","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,31]]},"article-number":"P1.58"}}