Article Dans Une Revue Journal of Graph Algorithms and Applications Année : 2025

Correcting a graph into a linegraph minimizing hamming distance edition is NP-complete and FPT by treewidth

Résumé

Since Beineke's work in 1968 on linegraphs, attention has focused on the classification of graphs as linegraphs. It is known that every graph $G$ is the linegraph of an hypergraph, and the question is to characterize that root graph. We introduce the $C_{p,q}$ classes, defined as sets of graphs where each vertex can be covered by at most $p$ cliques, and each edge belongs to at most $q$ cliques. These classes provide a comprehensive classification of linegraphs through a unified and parameterized approach. They describe previously known graph classes - such as linegraphs of simple graphs, $p$-uniform hypergraphs and $p$-uniform $1$-linear hypergraphs - while being capable of generalization. We study the complexity of determining the membership and edit distance of a graph to one of these classes. We prove the first Fixed Parameter Tractable algorithm with respect to treewidth to compute the edit distance.

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hal-05051712 , version 1 (29-04-2025)

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Dominique Barth, Dimitri Watel, Marc-Antoine Weisser. Correcting a graph into a linegraph minimizing hamming distance edition is NP-complete and FPT by treewidth. Journal of Graph Algorithms and Applications, 2025, 29 (1), pp.63-90. ⟨10.7155/jgaa.v29i1.3029⟩. ⟨hal-05051712⟩
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