| 1. |
- Bandelt, HJ, et al.
(författare)
-
Quasi-median graphs from sets of partitions
- 2002
-
Ingår i: Discrete Applied Mathematics. - 0166-218X .- 1872-6771. ; 122:23-35, s. 23-35
-
Tidskriftsartikel (populärvet., debatt m.m.)abstract
- In studies of molecular evolution, one is typically confronted with the task of inferring a phylogenetic tree from a set X of sequences of length n over a finite alphabet Lambda. For studies that invoke parsimony, it has been found helpful to consider the quasi-median graph generated by X in the Hamming graph Lambda(n). Although a great deal is already known about quasi-median graphs (and their algebraic counterparts), little is known about the quasi-median generation in Lambda(n) starting from a set X of vertices. We describe the vertices of the quasi-median graph generated by X in terms of the coordinatewise partitions of X. In particular, we clarify when the generated quasi-median graph is the so-called relation graph associated with X. This immediately characterizes the instances where either a block graph or the total Hamming graph is generated.
|
|
| 2. |
- Cieslik, D, et al.
(författare)
-
Connectivity calculus
- 2003
-
Ingår i: Applied Mathematics Letters. - 0893-9659 .- 1873-5452. ; 16:3, s. 395-399
-
Tidskriftsartikel (refereegranskat)abstract
- Given a finite hypergraph H = (V, E) and, for each e E E, a collection of nonempty subsets pi(e) of e, Mobius inversion is used to establish a recursive formula for the number of connected components of the hypergraph H = (V, boolean OR(eis an element ofE)pi(e)). As shown elsewhere, this formula is an essential ingredient in the context of a certain divide-and-conquer strategy that allows us to define a dynamical programming scheme solving Steiner's problem for graphs in linear time (however, with a constant depending hyperexponentially on their tree width).
|
|
| 3. |
- Cieslik, D., et al.
(författare)
-
Connectivity calculus
- 2003
-
Ingår i: Applied Mathematical Letters. ; 16, s. 395-399
-
Tidskriftsartikel (refereegranskat)
|
|
| 4. |
- Dress, A., et al.
(författare)
-
Affine maps that induce polyhedral complex isomorphisms
- 2000
-
Ingår i: Discrete & Computational Geometry. - 0179-5376 .- 1432-0444. ; 24:1, s. 49-60
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper we show that an affine bijection f: T-1 --> T-2 between two polyhedral complexes T-1, T-2, both of which consist of a union of faces of two convex polyhedra P-1 and P-2, necessarily respects the cell-complex structure of T-1 and T-2 inherited from P-1 and P-2, respectively, provided f extends to an affine map from P-1 into P-2. In addition, we present an application of this result within the area of T-theory to obtain a far-reaching generalization of previous results regarding the equivalence of two distinct constructions of the phylogenetic tree associated to "perfect" (that is, treelike) distance data.
|
|
| 5. |
|
|
| 6. |
- Dress, A, et al.
(författare)
-
Antipodal metrics and split systems
- 2002
-
Ingår i: European Journal of Combinatorics. - : Elsevier BV. - 0195-6698 .- 1095-9971. ; 23:2, s. 187-200
-
Tidskriftsartikel (refereegranskat)abstract
- Recall that a metric d on a finite set X is called antipodal if there exists a map sigma : X --> X: x --> (x) over bar so that d(x, (x) over bar) = d(x, y) + d(y, (x) over bar) holds for all x, y epsilon X. Antipodal metrics canonically arise as metrics induced on specific weighted graphs, although their abundance becomes clearer in light of the fact that any finite metric space can be isometrically embedded in a more or less canonical way into an antipodal metric space called its full antipodal extension. In this paper, we examine in some detail antipodal metrics that are, in addition, totally split decomposable. In particular, we give an explicit characterization of such metrics, and prove that-somewhat surprisingly-the full antipodal extension of a proper metric d on a finite set X is totally split decomposable if and only if d is linear or #X = 3 holds.
|
|
| 7. |
- Dress, A., et al.
(författare)
-
Six points suffice : How to check for metric consistency
- 2001
-
Ingår i: European journal of combinatorics (Print). - : Elsevier BV. - 0195-6698 .- 1095-9971. ; 22:4, s. 465-474
-
Tidskriftsartikel (refereegranskat)abstract
- In many areas of data analysis, it is desirable to have tools at hand for analyzing the structure of distance tables-or, in more mathematical terms, of finite metric spaces. One such tool, known as split decomposition theory has proven particularly useful in this respect. Tbe class of so-called totally decomposable metrics forms a cornerstone for this theory, and much work has been devoted to their study. Recently, it has become apparent that a particular subclass of these metrics, the consistent metrics, are also of fundamental importance. In this paper, we give a six-point characterization of consistent metrics amongst the totally decomposable ones.
|
|
| 8. |
- Gutman, I., et al.
(författare)
-
Estimating and approximating the total pi-electron energy of benzenoid hydrocarbons
- 2000
-
Ingår i: Zeitschrift fur Naturforschung A-A Journal of Physical Sciences. - 0932-0784 .- 1865-7109. ; 55:5, s. 507-512
-
Tidskriftsartikel (refereegranskat)abstract
- Lower and upper bounds as well as approximate formulas for the total pi-electron energy (E) of benzenoid hydrocarbons are deduced, depending only on the number of carbon atoms (n) and number of carbon-carbon bonds (m). These are better than the several previously known (n, m)-type estimates and approximations for E.
|
|
| 9. |
|
|
| 10. |
|
|
