DeepAI AI Chat
Log In Sign Up

Detecting and Enumerating Small Induced Subgraphs in c-Closed Graphs

by   Tomohiro Koana, et al.
Berlin Institute of Technology (Technische Universität Berlin)

Fox et al. [SIAM J. Comp. 2020] introduced a new parameter, called c-closure, for a parameterized study of clique enumeration problems. A graph G is c-closed if every pair of vertices with at least c common neighbors is adjacent. The c-closure of G is the smallest c such that G is c-closed. We systematically explore the impact of c-closure on the computational complexity of detecting and enumerating small induced subgraphs. More precisely, for each graph H on three or four vertices, we investigate parameterized polynomial-time algorithms for detecting H and for enumerating all occurrences of H in a given c-closed graph.


page 1

page 2

page 3

page 4


Exploiting 𝐜-Closure in Kernelization Algorithms for Graph Problems

A graph is c-closed if every pair of vertices with at least c common nei...

Computing Dense and Sparse Subgraphs of Weakly Closed Graphs

A graph G is weakly γ-closed if every induced subgraph of G contains one...

FPT Algorithms for Finding Dense Subgraphs in c-Closed Graphs

Dense subgraph detection is a fundamental problem in network analysis fo...

Computing metric hulls in graphs

We prove that, given a closure function the smallest preimage of a close...

Finding Cliques in Social Networks: A New Distribution-Free Model

We propose a new distribution-free model of social networks. Our definit...

Essentially Tight Kernels for (Weakly) Closed Graphs

We study kernelization of classic hard graph problems when the input gra...

Algebraic Branching Programs, Border Complexity, and Tangent Spaces

Nisan showed in 1991 that the width of a smallest noncommutative single-...