@misc{BeisegelChiarelliKoehleretal., author = {Beisegel, Jesse and Chiarelli, Nina and K{\"o}hler, Ekkehard and Krnc, Matjaž and Milanič, Martin and Pivač, Nevena and Scheffler, Robert and Strehler, Martin}, title = {Edge Elimination and Weighted Graph Classes}, series = {Graph-Theoretic Concepts in Computer Science - 46th International Workshop, {WG} 2020, Leeds, UK, June 24-26, 2020}, journal = {Graph-Theoretic Concepts in Computer Science - 46th International Workshop, {WG} 2020, Leeds, UK, June 24-26, 2020}, editor = {Adler, Isolde and M{\"u}ller, Haiko}, publisher = {Springer}, address = {Cham}, isbn = {978-3-030-60439-4}, issn = {1611-3349}, doi = {10.1007/978-3-030-60440-0_11}, pages = {134 -- 147}, language = {en} } @misc{BeisegelKoehlerScheffleretal., author = {Beisegel, Jesse and K{\"o}hler, Ekkehard and Scheffler, Robert and Strehler, Martin}, title = {Linear Time LexDFS on Chordal Graphs}, series = {28th Annual European Symposium on Algorithms (ESA) 2020, September 7-9, 2020, Pisa, Italy)}, volume = {173}, journal = {28th Annual European Symposium on Algorithms (ESA) 2020, September 7-9, 2020, Pisa, Italy)}, publisher = {Schloss Dagstuhl, Leibnitz Zentrum f{\"u}r Informatik}, doi = {10.4230/LIPIcs.ESA.2020.13}, url = {http://nbn-resolving.de/urn:nbn:de:0030-drops-128790}, pages = {13:1 -- 13:13}, language = {en} } @misc{BeisegelRatajczakScheffler, author = {Beisegel, Jesse and Ratajczak, Fabienne and Scheffler, Robert}, title = {Computing hamiltonian paths with partial order restrictions}, series = {ACM Transactions on Computation Theory}, volume = {17}, journal = {ACM Transactions on Computation Theory}, number = {1}, issn = {1942-3454}, doi = {10.1145/3711844}, pages = {1 -- 24}, abstract = {When solving the Hamiltonian path problem it seems natural to be given additional precedence constraints for the order in which the vertices are visited. For example, one could decide whether a Hamiltonian path exists for a fixed starting point, or that some vertices are visited before another vertex. We consider the problem of finding a Hamiltonian path that observes all precedence constraints given in a partial order on the vertex set. We show that this problem is NP-complete even if restricted to complete bipartite graphs and posets of height 2. In contrast, for posets of width k there is a known O(k^2 n^k) algorithm for arbitrary graphs with n vertices. We show that it is unlikely that the running time of this algorithm can be improved significantly, i.e., there is no f(k) n^o(k) time algorithm under the assumption of the Exponential Time Hypothesis. Furthermore, for the class of outerplanar graphs, we give an O(n^2) algorithm for arbitrary posets.}, language = {en} } @misc{BeisegelKlostKnorretal., author = {Beisegel, Jesse and Klost, Katharina and Knorr, Kristin and Ratajczak, Fabienne and Scheffler, Robert}, title = {A graph width perspective on partially ordered Hamiltonian paths and cycles II : vertex and edge deletion numbers}, series = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)}, journal = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)}, editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{\"u}r Informatik}, address = {Wadern}, isbn = {978-3-95977-407-9}, doi = {10.4230/LIPIcs.IPEC.2025.30}, url = {http://nbn-resolving.de/urn:nbn:de:0030-drops-251623}, pages = {30:1 -- 30:19}, abstract = {We consider the problem of finding a Hamiltonian path or cycle with precedence constraints in the form of a partial order on the vertex set. We study the complexity for graph width parameters for which the ordinary problems Hamiltonian Path and Hamiltonian Cycle are in FPT. In particular, we focus on parameters that describe how many vertices and edges have to be deleted to become a member of a certain graph class. We show that the problems are W[1]-hard for such restricted cases as vertex distance to path and vertex distance to clique. We complement these results by showing that the problems can be solved in XP time for vertex distance to outerplanar and vertex distance to block. Furthermore, we present some FPT algorithms, e.g., for edge distance to block. Additionally, we prove para-NP-hardness when considered with the edge clique cover number.}, language = {en} }