{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:06:38Z","timestamp":1775052398796,"version":"3.50.1"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2012,6]]},"abstract":"<jats:p> Let G be a graph. The point arboricity of G, denoted by \u03c1(G), is the minimum number of colors that can be used to color the vertices of G so that each color class induces an acyclic subgraph of G. Borodin et al. (Discrete Math.214 (2000) 101\u2013112) first introduced the list point arboricity of G, denoted by \u03c1<jats:sub>l<\/jats:sub>(G). We prove that for any graph G, [Formula: see text], where deg (G) denotes the degeneracy of G, that is, the minimum number k such that \u03b4(H) \u2264 k for any subgraph H of G. Using this upper bound, we show that \u03c1<jats:sub>l<\/jats:sub>(G) \u2264 3 for any planar graph G. In particular, if either G is K<jats:sub>4<\/jats:sub>-minor free, or for an integer k \u2208 {3, 4, 5, 6}, G is planar and does not contain k-cycles, then \u03c1<jats:sub>l<\/jats:sub>(G) \u2264 2. For any graph G of order n, [Formula: see text]. In addition, we provide a new proof of a theorem of Borodin et al., which states that if G is neither a complete graph of odd order nor a cycle then [Formula: see text]. Finally, we show that la (G) = lla (G) = 2 if G is 3-regular, and la (G) = lla (G) = 3 if G is 4-regular, where la (G) is the linear arboricity of G and lla (G) is list linear arboricity of G which is introduced recently by An and Wu. <\/jats:p>","DOI":"10.1142\/s1793830912500279","type":"journal-article","created":{"date-parts":[[2012,6,19]],"date-time":"2012-06-19T14:55:53Z","timestamp":1340117753000},"page":"1250027","source":"Crossref","is-referenced-by-count":4,"title":["LIST POINT ARBORICITY OF GRAPHS"],"prefix":"10.1142","volume":"04","author":[{"given":"NINI","family":"XUE","sequence":"first","affiliation":[{"name":"College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang, 830046, P. R. China"},{"name":"College of Information Engineering, Tarim University, Alar, Xinjiang 843300, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"BAOYINDURENG","family":"WU","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Tarim University, Alar, Xinjiang 843300, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,6,21]]},"reference":[{"key":"rf1","first-page":"1","volume":"2","author":"Akiyama J.","journal-title":"Bull. Liber. Arts Sci. NMS"},{"key":"rf2","first-page":"405","volume":"30","author":"Akiyama J.","journal-title":"Math. Slovaca"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230110108"},{"key":"rf4","first-page":"499","author":"An X.","journal-title":"Discuss. Math. Graph Theory (3)"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"rf6","first-page":"183","volume":"12","author":"Borodin O. V.","journal-title":"J. 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