{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T14:12:57Z","timestamp":1773583977279,"version":"3.50.1"},"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>A proper coloring of the vertices of a graph is called a star coloring if every two color classes induce a star forest. Star colorings are a strengthening of acyclic colorings, i.e., proper colorings in which every two color classes induce a forest. We show that every acyclic $k$-coloring can be refined to a star coloring with at most $(2k^2-k)$ colors.  Similarly, we prove that planar graphs have star colorings with at most 20 colors and we exhibit a planar graph which requires 10 colors.  We prove several other structural and topological results for star colorings, such as: cubic graphs are $7$-colorable, and planar graphs of girth at least $7$ are $9$-colorable. We provide a short proof of the result of Fertin, Raspaud, and Reed that graphs with tree-width $t$ can be star colored with ${t+2\\choose2}$ colors, and we show that this is best possible.<\/jats:p>","DOI":"10.37236\/1779","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:22:45Z","timestamp":1578720165000},"source":"Crossref","is-referenced-by-count":88,"title":["Coloring with no $2$-Colored $P_4$'s"],"prefix":"10.37236","volume":"11","author":[{"given":"Michael O.","family":"Albertson","sequence":"first","affiliation":[]},{"given":"Glenn G.","family":"Chappell","sequence":"additional","affiliation":[]},{"given":"H. A.","family":"Kierstead","sequence":"additional","affiliation":[]},{"given":"Andr\u00e9","family":"K\u00fcndgen","sequence":"additional","affiliation":[]},{"given":"Radhika","family":"Ramamurthi","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,3,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r26\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r26\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:04:06Z","timestamp":1579323846000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r26"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,3,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1779","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,3,31]]},"article-number":"R26"}}