{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T08:01:47Z","timestamp":1769155307595,"version":"3.49.0"},"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>Given a graph $G$ and an integer $d\\ge 0$, its $d$-defective chromatic number\u00a0$\\chi^d(G)$ is the smallest size of a partition of the vertices into parts inducing subgraphs with maximum degree at most $d$. Guo, Kang and Zwaneveld recently studied the relationship between the $d$-defective chromatic number of the $(d+1)$-fold (clique) blowup $G\\boxtimes K_{d+1}$ of a graph $G$ and its ordinary chromatic number, and conjectured that $\\chi(G)=\\chi^d(G\\boxtimes K_{d+1})$ for every graph $G$ and $d\\ge 0$. In this note we disprove this conjecture by constructing graphs $G$ of arbitrarily large chromatic number such that $\\chi(G)\\ge \\frac{30}{29}\\chi^d(G\\boxtimes K_{d+1})$ for infinitely many $d$. On the positive side, we show that the conjecture holds with a constant factor correction, namely $\\chi^d(G\\boxtimes K_{d+1})\\le \\chi(G)\\le 2\\chi^d(G\\boxtimes K_{d+1})$ for every graph $G$ and $d\\ge 0$.<\/jats:p>","DOI":"10.37236\/14039","type":"journal-article","created":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T16:52:43Z","timestamp":1769100763000},"source":"Crossref","is-referenced-by-count":0,"title":["Defective Coloring of Blowups"],"prefix":"10.37236","volume":"33","author":[{"given":"Sergey","family":"Norin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Raphael","family":"Steiner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2026,1,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p17\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p17\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T16:52:44Z","timestamp":1769100764000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i1p17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,23]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/14039","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,23]]},"article-number":"P1.17"}}