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 ∈ 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 O(k⁵) vertices. This answers an open question posed by Falk Hüffner at Workshop on Kernels (WorKer) in 2013.
@InProceedings{eiben_et_al:LIPIcs.ESA.2020.42, author = {Eiben, Eduard and Lochet, William}, title = {{A Polynomial Kernel for Line Graph Deletion}}, booktitle = {28th Annual European Symposium on Algorithms (ESA 2020)}, pages = {42:1--42:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-162-7}, ISSN = {1868-8969}, year = {2020}, volume = {173}, editor = {Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.42}, URN = {urn:nbn:de:0030-drops-129088}, doi = {10.4230/LIPIcs.ESA.2020.42}, annote = {Keywords: Kernelization, line graphs, H-free editing, graph modification problem} }
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