A Polynomial Kernel for Line Graph Deletion
Abstract
The line graph of a graph $G$ is the graph $L(G)$ whose vertex set is the edge set of $G$ and there is an edge between $e,f\in E(G)$ if $e$ and $f$ share an endpoint in $G$. A graph is called line graph if it is a line graph of some graph. We study the Line-Graph-Edge Deletion problem, which asks whether we can delete at most $k$ edges from the input graph $G$ such that the resulting graph is a line graph. More precisely, we give a polynomial kernel for Line-Graph-Edge Deletion with $\mathcal{O}(k^{5})$ vertices. This answers an open question posed by Falk Hüffner at Workshop on Kernels (WorKer) in 2013.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2020
- DOI:
- 10.48550/arXiv.2006.15584
- arXiv:
- arXiv:2006.15584
- Bibcode:
- 2020arXiv200615584E
- Keywords:
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- Computer Science - Data Structures and Algorithms
- E-Print:
- To be published in the Proceedings of the 28th Annual European Symposium on Algorithms (ESA 2020)