DeepAI AI Chat
Log In Sign Up

Detecting and Enumerating Small Induced Subgraphs in c-Closed Graphs

07/23/2020
by   Tomohiro Koana, et al.
Berlin Institute of Technology (Technische Universität Berlin)
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

05/08/2020

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...
07/10/2020

Computing Dense and Sparse Subgraphs of Weakly Closed Graphs

A graph G is weakly γ-closed if every induced subgraph of G contains one...
07/19/2020

FPT Algorithms for Finding Dense Subgraphs in c-Closed Graphs

Dense subgraph detection is a fundamental problem in network analysis fo...
10/09/2017

Computing metric hulls in graphs

We prove that, given a closure function the smallest preimage of a close...
04/20/2018

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

We propose a new distribution-free model of social networks. Our definit...
03/05/2021

Essentially Tight Kernels for (Weakly) Closed Graphs

We study kernelization of classic hard graph problems when the input gra...
03/10/2020

Algebraic Branching Programs, Border Complexity, and Tangent Spaces

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