{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T14:12:43Z","timestamp":1780668763453,"version":"3.54.1"},"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>For $0 \\leq \\alpha &lt; 1$, the $\\alpha$-spectral radius of a graph $G$ is defined as the largest eigenvalue of $A_{\\alpha}(G)=\\alpha D(G)+(1-\\alpha)A(G)$, where $D(G)$ and $A(G)$ are the diagonal matrix of degrees and adjacency matrix of $G$, respectively. A graph is called color-critical if it contains an edge whose deletion reduces its chromatic number. The celebrated Erd\\H{o}s-Stone-Simonovits theorem asserts that $ \\mathrm{ex}(n,\\mathcal{F})=\\left(1-\\frac{1}{\\chi(\\mathcal{F})-1}+o(1)\\right)\\frac{n^2}{2},$ where $\\chi(\\mathcal{F})$ is the chromatic number of $\\mathcal{F}$. Nikiforov and Zheng et al. established the adjacency spectral and signless Laplacian spectral versions of this theorem, respectively. In this paper, we present the $\\alpha$-spectral version of this theorem, which unifies the aforementioned results. Furthermore, we characterize the $\\alpha$-spectral extremal graphs for color-critical graphs, thereby extending the existing results on adjacency spectral and signless Laplacian spectral extremal graphs for such graphs.<\/jats:p>","DOI":"10.37236\/14952","type":"journal-article","created":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T13:31:26Z","timestamp":1780666286000},"source":"Crossref","is-referenced-by-count":0,"title":["The $\\alpha$-Spectral Tur\u00e1n Type Problems for Graphs"],"prefix":"10.37236","volume":"33","author":[{"given":"Jiadong","family":"Wu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yongchun","family":"Lu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liying","family":"Kang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2026,6,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i2p48\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i2p48\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T13:31:27Z","timestamp":1780666287000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i2p48"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,5]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,4,14]]}},"URL":"https:\/\/doi.org\/10.37236\/14952","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,5]]},"article-number":"P2.48"}}