{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T19:49:53Z","timestamp":1767988193168,"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>Kempe equivalence is a classical and important notion on vertex coloring in graph theory. In the present paper, we introduce several ideals associated with graphs and provide a method for determining whether two $k$-colorings are Kempe equivalent via commutative algebra. Moreover, we give a way to compute all $k$-colorings of a graph up to Kempe equivalence by virtue of the algebraic technique on Gr\u00f6bner bases. As a consequence, the number of $k$-Kempe classes can be computed by using Hilbert functions. Finally, we introduce several algebraic algorithms related to Kempe equivalence.<\/jats:p>","DOI":"10.37236\/13183","type":"journal-article","created":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T14:32:29Z","timestamp":1767969149000},"source":"Crossref","is-referenced-by-count":0,"title":["Examining Kempe Equivalence via Commutative Algebra"],"prefix":"10.37236","volume":"33","author":[{"given":"Hidefumi","family":"Ohsugi","sequence":"first","affiliation":[]},{"given":"Akiyoshi","family":"Tsuchiya","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2026,1,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T14:32:29Z","timestamp":1767969149000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i1p8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,9]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/13183","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,9]]},"article-number":"P1.8"}}