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• W2026720321 abstract "We study a family of problems where the goal is to make a graph Eulerian, i.e., connected and with all the vertices having even degrees, by a minimum number of deletions. We completely classify the parameterized complexity of various versions: undirected or directed graphs, vertex or edge deletions, with or without the requirement of connectivity, etc. The collection of results shows an interesting contrast: while the node-deletion variants remain intractable, i.e., W[1]-hard for all the studied cases, edge-deletion problems are either fixed-parameter tractable or polynomial-time solvable. Of particular interest is a randomized FPT algorithm for making an undirected graph Eulerian by deleting the minimum number of edges, based on a novel application of the color coding technique. For versions that remain NP-complete but fixed-parameter tractable we consider also possibilities of polynomial kernelization; unfortunately, we prove that this is not possible unless NP⊆coNP/poly." @default.
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• W2026720321 date "2012-06-22" @default.
• W2026720321 modified "2023-09-23" @default.
• W2026720321 title "Parameterized Complexity of Eulerian Deletion Problems" @default.
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• W2026720321 doi "https://doi.org/10.1007/s00453-012-9667-x" @default.
• W2026720321 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/3883159" @default.
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