Abstract
For two planar undirected graphs $G$ and $H$, the {\it subgraphs recognition problem} (SRP) is to find and list all subgraphs of $G$ which are isomorphic to $H$. In this paper, we introduce the idea of layer-decomposition with degree and present an algorithm based on this idea for SRP. Since subgraphs isomorphic to each other contain their spanning trees with the same decomposition, the SRP can be decomposed into two subproblems: First, find subtrees of $G$ which have the same layer-decomposition as that of $H$. Then, test whether the induced subgraphs generated by these subtrees are isomorphic to $H$. By this scheme, we greatly decrease the complexity to $O(n(\Delta-1)^{k-1}k^2)$, where $\Delta$ is the degree of $G$ and $n, k$ are the orders of $G, H$ respectively.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
