On the vertex-arboricity of planar graphs
European Journal of Combinatorics
Fractional vertex arboricity of graphs
CJCDGCGT'05 Proceedings of the 7th China-Japan conference on Discrete geometry, combinatorics and graph theory
Discrete Applied Mathematics
Vertex-arboricity of planar graphs without intersecting triangles
European Journal of Combinatorics
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In this paper, we study the critical point-arboricity graphs. We prove two lower bounds for the number of edges of k-critical point-arboricity graphs. A theorem of Kronk is extended by proving that the point-arboricity of a graph G embedded on a surface S with Euler genus g = 2, 5, 6 or g ≥ 10 is at most $k =\lfloor {9 +\sqrt {1+ 24\, g}\over 4}\rfloor$ with equality holding iff G contains either K2k-1 or K2k-4 + C5 as a subgraph. It is also proved that locally planar graphs have point-arboricity ≤ 3 and that triangle-free locally planar-graphs have point-arboricity ≤ 2. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 50–61, 2002