1. Reachability relations, transitive digraphs and groupsAleksander Malnič, Primož Potočnik, Norbert Seifter, Primož Šparl, 2015, izvirni znanstveni članek Opis: In [A. Malnič, D. Marušič, N. Seifter, P. Šparl and B. Zgrablič, Reachability relations in digraphs, Europ. J. Combin. 29 (2008), 1566-1581] it was shown that properties of digraphs such as growth, property ▫$\mathbf{Z}$▫, and number of ends are reflected by the properties of certain reachability relations defined on the vertices of the corresponding digraphs. In this paper we study these relations in connection with certain properties of automorphism groups of transitive digraphs. In particular, one of the main results shows that if atransitive digraph admits a nilpotent subgroup of automorphisms with finitely many orbits, then its nilpotency class and the number of orbits are closely related to particular properties of reachability relations defined on the digraphs in question. The obtained results have interesting implications for Cayley digraphs of certain types of groups such as torsion-free groups of polynomial growth. Ključne besede: Cayley digraph, reachability relation Objavljeno v RUP: 31.12.2021; Ogledov: 889; Prenosov: 16 Celotno besedilo (311,92 KB) |
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4. Perfect phylogenies via branchings in acyclic digraphs and a generalization of Dilworth's theoremAdemir Hujdurović, Martin Milanič, Edin Husić, Romeo Rizzi, Alexandru I. Tomescu, 2017, objavljeni povzetek znanstvenega prispevka na konferenci Ključne besede: perfect phylogeny, NP-hard problem, branching, acyclic digraph, chain partition, Dilworth's theorem, min-max theorem, approximation algorithm, heuristic Objavljeno v RUP: 17.09.2018; Ogledov: 2025; Prenosov: 119 Povezava na celotno besedilo |
5. Reconstructing perfect phylogenies via binary matrices, branchings in DAGs, and a generalization of Dilworth's theoremAdemir Hujdurović, Martin Milanič, Edin Husić, Romeo Rizzi, Alexandru I. Tomescu, 2018, objavljeni povzetek znanstvenega prispevka na konferenci Ključne besede: perfect phylogeny, NP-hard problem, branching, acyclic digraph, chain partition, Dilworth's theorem, min-max theorem, approximation algorithm, heuristic Objavljeno v RUP: 17.09.2018; Ogledov: 1951; Prenosov: 78 Celotno besedilo (1,44 MB) Gradivo ima več datotek! Več... |
6. Reconstructing perfect phylogenies via binary matrices, branchings in DAGs, and a generalization of Dilworth's theoremMartin Milanič, 2018, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje) Ključne besede: perfect phylogeny, NP-hard problem, graph coloring, branching, acyclic digraph, chain partition, Dilworth's theorem, min-max theorem, approximation algorithm, heuristic Objavljeno v RUP: 17.09.2018; Ogledov: 1936; Prenosov: 20 Povezava na celotno besedilo |
7. MIPUP : minimum perfect unmixed phylogenies for multi-sampled tumors via branchings and ILPEdin Husić, Xinyue Li, Ademir Hujdurović, Miika Mehine, Romeo Rizzi, Veli Mäkinen, Martin Milanič, Alexandru I. Tomescu, 2018, izvirni znanstveni članek Ključne besede: perfect phylogeny, minimum conflict-free row split problem, branching, acyclic digraph, integer linear programming Objavljeno v RUP: 17.09.2018; Ogledov: 2093; Prenosov: 112 Povezava na celotno besedilo |
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9. Perfect phylogenies via branchings in acyclic digraphs and a generalization of Dilworth's theoremAdemir Hujdurović, Edin Husić, Martin Milanič, Romeo Rizzi, Alexandru I. Tomescu, 2018, izvirni znanstveni članek Ključne besede: perfect phylogeny, minimum conflict-free row split problem, branching, acyclic digraph, chain partition, Dilworth's theorem, min-max theorem, approximation algorithm, APXhardness Objavljeno v RUP: 08.05.2018; Ogledov: 2402; Prenosov: 154 Povezava na celotno besedilo |
10. Reachability relations in digraphsAleksander Malnič, Dragan Marušič, Norbert Seifter, Primož Šparl, Boris Zgrablić, 2008, izvirni znanstveni članek Opis: In this paper we study reachability relations on vertices of digraphs, informally defined as follows. First, the weight of a walk is equal to the number of edges traversed in the direction coinciding with their orientation, minus the number of edges traversed in the direction opposite to their orientation. Then, a vertex ▫$u$▫ is ▫$R_k^+$▫-related to a vertex ▫$v$▫ if there exists a 0-weighted walk from ▫$u$▫ to ▫$v$▫ whose every subwalk starting at u has weight in the interval ▫$[0,k]$▫. Similarly, a vertex ▫$u$▫ is ▫$R_k^-$▫-related to a vertex ▫$v$▫ if there exists a 0-weighted walk from ▫$u$▫ to ▫$v$▫ whose every subwalk starting at ▫$u$▫ has weight in the interval ▫$[-k,0]$▫. For all positive integers ▫$k$▫, the relations ▫$R_k^+$▫ and ▫$R_k^-$▫ are equivalence relations on the vertex set of a given digraph. We prove that, for transitive digraphs, properties of these relations are closely related to other properties such as having property ▫$\mathbb{Z}$▫, the number of ends, growth conditions, and vertex degree. Ključne besede: graph theory, digraph, reachability relations, end of a graph, property ▫$\mathbb{Z}$▫, growth Objavljeno v RUP: 03.04.2017; Ogledov: 2797; Prenosov: 133 Povezava na celotno besedilo |