{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:05Z","timestamp":1753893845255,"version":"3.41.2"},"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>The square $G^2$ of a graph $G$ is the graph defined on $V(G)$ such that two vertices $u$ and $v$ are adjacent in $G^2$ if the distance between $u$ and $v$ in $G$ is at most 2. Let $\\chi(H)$ and $\\chi_{\\ell}(H)$ be the chromatic number and the list chromatic number of $H$, respectively. A graph $H$ is called chromatic-choosable if $\\chi_{\\ell} (H) = \\chi(H)$. It is an interesting problem to find graphs that are chromatic-choosable.Motivated by the List Total Coloring Conjecture, Kostochka and Woodall (2001) proposed the List Square Coloring Conjecture which states that $G^2$ is chromatic-choosable for every graph $G$. Recently, Kim and Park showed that the List Square Coloring Conjecture does not hold in general by finding a family of graphs whose squares are complete multipartite graphs and are not chromatic choosable. It is a well-known fact that the List Total Coloring Conjecture is true if the List Square Coloring Conjecture holds for special class of bipartite graphs. Hence a natural question is whether $G^2$ is chromatic-choosable or not for every bipartite graph $G$.In this paper, we give a bipartite graph $G$ such that $\\chi_{\\ell} (G^2) \\neq \\chi(G^2)$. Moreover, we show that the value $\\chi_{\\ell}(G^2) - \\chi(G^2)$ can be arbitrarily large.<\/jats:p>","DOI":"10.37236\/4343","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:31:33Z","timestamp":1578702693000},"source":"Crossref","is-referenced-by-count":1,"title":["Bipartite Graphs whose Squares are not Chromatic-Choosable"],"prefix":"10.37236","volume":"22","author":[{"given":"Seog-Jin","family":"Kim","sequence":"first","affiliation":[]},{"given":"Boram","family":"Park","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,2,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p46\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p46\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:25:15Z","timestamp":1579256715000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i1p46"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/4343","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,2,25]]},"article-number":"P1.46"}}