EÆciently Computing Vertex Arboricity of Planar Graphs
نویسندگان
چکیده
Acyclic-coloring of a graph G = (V;E) is a partitioning of V , such that the induced subgraph of each partition is acyclic. The minimumnumber of such partitions of V is de ned as the vertex arboricity of G. An O(n) algorithm (n = jV j) for acyclic-coloring of planar graphs with 3 colors is presented. Next, an O(n) heuristic is proposed which produces a valid acyclic-2-coloring of a planar graph, if one exists (since there are planar graphs with arboricity 3). We also prove that our heuristic is guaranteed to produce a valid acyclic-2-coloring for all outerplanar graphs (which are of arboricity 2) in O(n) time. Finally, some experimental results for our acyclic 3-coloring and 2-coloring algorithms, along with future directions are presented.
منابع مشابه
Eeciently Computing Vertex Arboricity of Planar Graphs
Acyclic-coloring of a graph G = (V; E) is a partitioning of V , such that the induced subgraph of each partition is acyclic. The minimum number of such partitions of V is deened as the vertex arboricity of G. An O(n) algorithm (n = jV j) for acyclic-coloring of planar graphs with 3 colors is presented. Next, an O(n 2) heuristic is proposed which produces a valid acyclic-2-coloring of a planar g...
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