{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T19:33:37Z","timestamp":1649187217185},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:p> The vertex arboricity [Formula: see text] of a graph [Formula: see text] is the minimum number of colors the vertices of the graph [Formula: see text] can be colored so that every color class induces an acyclic subgraph of [Formula: see text]. There are many results on the vertex arboricity of planar graphs. In this paper, we replace planar graphs with graphs which can be embedded in a surface [Formula: see text] of Euler characteristic [Formula: see text]. We prove that for the graph [Formula: see text] which can be embedded in a surface [Formula: see text] of Euler characteristic [Formula: see text] if no [Formula: see text]-cycle intersects a [Formula: see text]-cycle, or no [Formula: see text]-cycle intersects a [Formula: see text]-cycle, then [Formula: see text] in addition to the [Formula: see text]-regular quadrilateral mesh. <\/jats:p>","DOI":"10.1142\/s1793830920500809","type":"journal-article","created":{"date-parts":[[2020,6,20]],"date-time":"2020-06-20T04:30:02Z","timestamp":1592627402000},"page":"2050080","source":"Crossref","is-referenced-by-count":0,"title":["Vertex arboricity of graphs embedded in a surface of non-negative Euler characteristic"],"prefix":"10.1142","volume":"12","author":[{"given":"Wenshun","family":"Teng","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Qingdao University, Qingdao 266071, P. R. 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