Work

The Complexity of Contracting Bipartite Graphs into Small Cycles

Year: 2025

Type: article

Abstract: For a positive integer $\ell \geq 3$, the $C_\ell$-Contractibility problem takes as input an undirected simple graph $G$ and determines whether $G$ can be transformed into a graph isomorphic to $C_\ell$ (the induced cycle on $\ell$ vertices) using only edge contractions. Brouwer and Veldman [JGT 1987] showed that $C_4$-Contractibility is NP-complete in general graphs. It is easy to verify that $C_3$-Contractibility is polynomial-time solvable. Dabrowski and Paulusma [IPL 2017] showed that $C_{\ell}$-Contractibility is \NP-complete\ on bipartite graphs for $\ell = 6$ and posed as open problems the status of the problem when $\ell$ is 4 or 5. In this paper, we show that both $C_5$-Contractibility and $C_4$-Contractibility are NP-complete on bipartite graphs.

Source: Discrete Mathematics & Theoretical Computer Science

DOI: 10.46298/dmtcs.14658

Authors: R. Krithika, Roohani Sharma, Prafullkumar Tale

Institutions: Indian Institute of Technology Palakkad, Institute for Basic Science, Indian Institute of Science Education and Research Pune

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: Department of Science and Technology, Ministry of Science and Technology, India, Science and Engineering Research Board

Award: G8775254736