Arboricity and Subgraph Listing Algorithms

  title={Arboricity and Subgraph Listing Algorithms},
  author={Norishige Chiba and Takao Nishizeki},
  journal={SIAM J. Comput.},
In this paper we introduce a new simple strategy into edge-searching of a graph, which is useful to the various subgraph listing problems. Applying the strategy, we obtain the following four algorithms. The first one lists all the triangles in a graph G in $O(a(G)m)$ time, where m is the number of edges of G and $a(G)$ the arboricity of G. The second finds all the quadrangles in $O(a(G)m)$ time. Since $a(G)$ is at most three for a planar graph G, both run in linear time for a planar graph. The… 

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