{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T07:22:36Z","timestamp":1760080956308,"version":"3.41.2"},"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>Product structure theorems are a collection of recent results that have been used to resolve a number of longstanding open problems on planar graphs and related graph classes. One particularly useful version states that every planar graph $G$ is contained in the strong product of a $3$-tree $H$, a path $P$, and a $3$-cycle $K_3$; written as $G\\subseteq H\\boxtimes P\\boxtimes K_3$. A number of researchers have asked if this theorem can be strengthened so that the maximum degree in $H$ can be bounded by a function of the maximum degree in $G$. We show that no such strengthening is possible. Specifically, we describe an infinite family $\\mathcal{G}$ of planar graphs of maximum degree $5$ such that, if an $n$-vertex member $G$ of $\\mathcal{G}$ is isomorphic to a subgraph of $H\\boxtimes P\\boxtimes K_c$ where $P$ is a path and $H$ is a graph of maximum degree $\\Delta$ and treewidth $t$, then $t\\Delta c \\ge 2^{\\Omega(\\sqrt{\\log\\log n})}$.<\/jats:p>","DOI":"10.37236\/11712","type":"journal-article","created":{"date-parts":[[2024,6,13]],"date-time":"2024-06-13T16:38:34Z","timestamp":1718296714000},"source":"Crossref","is-referenced-by-count":1,"title":["Bounded-Degree Planar Graphs Do Not Have Bounded-Degree Product Structure"],"prefix":"10.37236","volume":"31","author":[{"given":"Vida","family":"Dujmovi\u0107","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gwena\u00ebl","family":"Joret","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Piotr","family":"Micek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pat","family":"Morin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Wood","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2024,6,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i2p51\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i2p51\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,13]],"date-time":"2024-06-13T16:38:34Z","timestamp":1718296714000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i2p51"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,14]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,4,5]]}},"URL":"https:\/\/doi.org\/10.37236\/11712","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2024,6,14]]},"article-number":"P2.51"}}