Vertex and Tree Arboricities of Graphs

Gerard J. Chang, Chiuyuan Chen, Yaping Chen
2004 Journal of combinatorial optimization  
This paper studies the following variations of arboricity of graphs. The vertex (respectively, tree) arboricity of a graph G is the minimum number va(G) (respectively, ta(G)) of subsets into which the vertices of G can be partitioned so that each subset induces a forest (respectively, tree). This paper studies the vertex and the tree arboricities on various classes of graphs for exact values, algorithms, bounds, hamiltonicity and NP-completeness. The graphs investigated in this paper include
more » ... ck-cactus graphs, series-parallel graphs, cographs and planar graphs.
doi:10.1023/b:joco.0000038912.82046.17 fatcat:zq75b47o3ffjjkd7s2r6r76gde