Computing the number of induced copies of a fixed graph in a bounded degree graph

Viresh Patel; Guus Regts

Computing the number of induced copies of a fixed graph in a bounded degree graph

Data Structures and Algorithms 2017-09-21 v2 Discrete Mathematics Combinatorics

Authors: Viresh Patel , Guus Regts

Abstract

In this paper we show that for any graph $H$ of order $m$ and any graph $G$ of order $n$ and maximum degree $\Delta$ one can compute the number of subsets $S$ of $V(G)$ that induces a graph isomorphic to $H$ in time $O(c^m\cdot n)$ for some constant $c = c(\Delta) > 0$ . This is essentially best possible.

Keywords

induced subgraph counting bounded degree graph fixed graph graph algorithm time complexity subgraph isomorphism

Cite

@article{arxiv.1707.05186,
  title  = {Computing the number of induced copies of a fixed graph in a bounded degree graph},
  author = {Viresh Patel and Guus Regts},
  journal= {arXiv preprint arXiv:1707.05186},
  year   = {2017}
}

Comments

In this version we have improved the running time from $O(c^m\cdot n^2)$ to $O(c^m\cdot n)$. To incorporate this, we had to apply some minor changes, mostly in Section 2, leaving the overall approach essentially unaffected. 10 pages

Computing the number of induced copies of a fixed graph in a bounded degree graph

Abstract

Keywords

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