1. Strong cliques in diamond-free graphsNina Chiarelli, Berenice Martínez-Barona, Martin Milanič, Jérôme Monnot, Peter Muršič, 2020, objavljeni znanstveni prispevek na konferenci Ključne besede: maximal clique, maximal stable set, diamond-free graph, strong clique, simplicial clique, CIS graph, NP-hard problem, linear-time algorithm, Erdős-Hajnal property Objavljeno v RUP: 10.11.2020; Ogledov: 1391; Prenosov: 38 Povezava na celotno besedilo |
2. Edge elimination and weighted graph classesJesse Beisegel, Nina Chiarelli, Ekkehard Köhler, Matjaž Krnc, Martin Milanič, Nevena Pivač, Robert Scheffler, Martin Strehler, 2020, objavljeni znanstveni prispevek na konferenci Ključne besede: edge elimination, weighted graph, split graph, threshold graph, chain graph, linear-time recognition algorithm Objavljeno v RUP: 10.11.2020; Ogledov: 1396; Prenosov: 34 Povezava na celotno besedilo |
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4. On split liftings with sectional complementsAleksander Malnič, Rok Požar, 2018, izvirni znanstveni članek Ključne besede: algorithm, Cayley voltages, covering projection, graph, group presentation, invariant section, lifting automorphisms, linear systems over the integers, split extension Objavljeno v RUP: 02.03.2018; Ogledov: 2508; Prenosov: 175 Povezava na celotno besedilo |
5. On the split structure of lifted groupsAleksander Malnič, Rok Požar, 2016, izvirni znanstveni članek Opis: Let ▫$\wp \colon \tilde{X} \to X$▫ be a regular covering projection of connected graphs with the group of covering transformations ▫$\rm{CT}_\wp$▫ being abelian. Assuming that a group of automorphisms ▫$G \le \rm{Aut} X$▫ lifts along $\wp$ to a group ▫$\tilde{G} \le \rm{Aut} \tilde{X}$▫, the problem whether the corresponding exact sequence ▫$\rm{id} \to \rm{CT}_\wp \to \tilde{G} \to G \to \rm{id}$▫ splits is analyzed in detail in terms of a Cayley voltage assignment that reconstructs the projection up to equivalence. In the above combinatorial setting the extension is given only implicitly: neither ▫$\tilde{G}$▫ nor the action ▫$G\to \rm{Aut} \rm{CT}_\wp$▫ nor a 2-cocycle ▫$G \times G \to \rm{CT}_\wp$▫, are given. Explicitly constructing the cover ▫$\tilde{X}$▫ together with ▫$\rm{CT}_\wp$▫ and ▫$\tilde{G}$▫ as permutation groups on ▫$\tilde{X}$▫ is time and space consuming whenever ▫$\rm{CT}_\wp$▫ is large; thus, using the implemented algorithms (for instance, HasComplement in Magma) is far from optimal. Instead, we show that the minimal required information about the action and the 2-cocycle can be effectively decoded directly from voltages (without explicitly constructing the cover and the lifted group); one could then use the standard method by reducing the problem to solving a linear system of equations over the integers. However, along these lines we here take a slightly different approach which even does not require any knowledge of cohomology. Time and space complexity are formally analyzed whenever ▫$\rm{CT}_\wp$▫ is elementary abelian. Ključne besede: algorithm, abelian cover, Cayley voltages, covering projection, graph, group extension, group presentation, lifting automorphisms, linear systems over the integers, semidirect product Objavljeno v RUP: 15.10.2015; Ogledov: 2767; Prenosov: 157 Celotno besedilo (422,56 KB) |