{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:04Z","timestamp":1753893844471,"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>Recently, Farnik asked whether the hat guessing number $\\mathrm{HG}(G)$ of a graph $G$ could be bounded as a function of its degeneracy $d$, and Bosek, Dudek, Farnik, Grytczuk and Mazur showed that $\\mathrm{HG}(G)\\ge 2^d$ is possible. We show that for all $d\\ge 1$ there exists a $d$-degenerate graph $G$ for which $\\mathrm{HG}(G) \\ge 2^{2^{d-1}}$. We also give a new general method for obtaining upper bounds on $\\mathrm{HG}(G)$. The question of whether $\\mathrm{HG}(G)$ is bounded as a function of $d$ remains open.<\/jats:p>","DOI":"10.37236\/9449","type":"journal-article","created":{"date-parts":[[2020,9,18]],"date-time":"2020-09-18T09:41:05Z","timestamp":1600422065000},"source":"Crossref","is-referenced-by-count":2,"title":["Hat Guessing Numbers of Degenerate Graphs"],"prefix":"10.37236","volume":"27","author":[{"given":"Xiaoyu","family":"He","sequence":"first","affiliation":[]},{"given":"Ray","family":"Li","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2020,9,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p58\/8177","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p58\/8177","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,18]],"date-time":"2020-09-18T09:41:05Z","timestamp":1600422065000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i3p58"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,10]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,7,9]]}},"URL":"https:\/\/doi.org\/10.37236\/9449","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,9,10]]},"article-number":"P3.58"}}