Counting Induced Subgraphs: An Algebraic Approach to #W[1]-Hardness

We study the problem # I N D S U B ( Φ ) of counting all induced subgraphs of size k in a graph G that satisfy the property Φ . It is shown that, given any graph property Φ that distinguishes independent sets from bicliques, # I N D S U B ( Φ ) is hard for the class # W [ 1 ] , i.e., the parameteriz...

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Bibliographic Details

Published in:	Algorithmica Vol. 84; no. 2; pp. 379 - 404
Main Authors:	Dörfler, Julian, Roth, Marc, Schmitt, Johannes, Wellnitz, Philip
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.02.2022 Springer Nature B.V
Subjects:	Algorithm Analysis and Problem Complexity Algorithms Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Graph theory Hardness Mathematics of Computing Theory of Computation Counting complexity Edge-transitive graphs Graph homomorphisms Induced subgraphs Parameterized complexity
ISSN:	0178-4617, 1432-0541
Online Access:	Get full text
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