1. Reachability relations, transitive digraphs and groupsAleksander Malnič, Primož Potočnik, Norbert Seifter, Primož Šparl, 2015, original scientific article Abstract: 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. Keywords: Cayley digraph, reachability relation Published in RUP: 31.12.2021; Views: 955; Downloads: 16 Full text (311,92 KB) |
2. |
3. |
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, published scientific conference contribution abstract Keywords: perfect phylogeny, NP-hard problem, branching, acyclic digraph, chain partition, Dilworth's theorem, min-max theorem, approximation algorithm, heuristic Published in RUP: 17.09.2018; Views: 2113; Downloads: 119 Link to full text |
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, published scientific conference contribution abstract Keywords: perfect phylogeny, NP-hard problem, branching, acyclic digraph, chain partition, Dilworth's theorem, min-max theorem, approximation algorithm, heuristic Published in RUP: 17.09.2018; Views: 2029; Downloads: 78 Full text (1,44 MB) This document has more files! More... |
6. Reconstructing perfect phylogenies via binary matrices, branchings in DAGs, and a generalization of Dilworth's theoremMartin Milanič, 2018, published scientific conference contribution abstract (invited lecture) Keywords: perfect phylogeny, NP-hard problem, graph coloring, branching, acyclic digraph, chain partition, Dilworth's theorem, min-max theorem, approximation algorithm, heuristic Published in RUP: 17.09.2018; Views: 2012; Downloads: 20 Link to full text |
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, original scientific article Keywords: perfect phylogeny, minimum conflict-free row split problem, branching, acyclic digraph, integer linear programming Published in RUP: 17.09.2018; Views: 2166; Downloads: 114 Link to full text |
8. |
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, original scientific article Keywords: perfect phylogeny, minimum conflict-free row split problem, branching, acyclic digraph, chain partition, Dilworth's theorem, min-max theorem, approximation algorithm, APXhardness Published in RUP: 08.05.2018; Views: 2472; Downloads: 155 Link to full text |
10. Reachability relations in digraphsAleksander Malnič, Dragan Marušič, Norbert Seifter, Primož Šparl, Boris Zgrablić, 2008, original scientific article Abstract: 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. Keywords: graph theory, digraph, reachability relations, end of a graph, property ▫$\mathbb{Z}$▫, growth Published in RUP: 03.04.2017; Views: 2847; Downloads: 133 Link to full text |