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Full-Text Articles in Physical Sciences and Mathematics
Rearrangement Operations On Unrooted Phylogenetic Networks, Remie Janssen, Jonathan Klawitter
Rearrangement Operations On Unrooted Phylogenetic Networks, Remie Janssen, Jonathan Klawitter
Theory and Applications of Graphs
Rearrangement operations transform a phylogenetic tree into another one and hence induce a metric on the space of phylogenetic trees. Popular operations for unrooted phylogenetic trees are NNI (nearest neighbour interchange), SPR (subtree prune and regraft), and TBR (tree bisection and reconnection). Recently, these operations have been extended to unrooted phylogenetic networks, which are generalisations of phylogenetic trees that can model reticulated evolutionary relationships. Here, we study global and local properties of spaces of phylogenetic networks under these three operations. In particular, we prove connectedness and asymptotic bounds on the diameters of spaces of different classes of phylogenetic networks, including …
Graphs Obtained From Collections Of Blocks, Colton Magnant, Pouria Salehi Nowbandegani, Hua Wang
Graphs Obtained From Collections Of Blocks, Colton Magnant, Pouria Salehi Nowbandegani, Hua Wang
Department of Mathematical Sciences Faculty Publications
Given a collection of d-dimensional rectangular solids called blocks, no two of which sharing interior points, construct a block graph by adding a vertex for each block and an edge if the faces of the two corresponding blocks intersect nontrivially. It is known that if d ≥ 3, such block graphs can have arbitrarily large chromatic number. We prove that the chromatic number can be bounded with only a mild restriction on the sizes of the blocks. We also show that block graphs of block configurations arising from partitions of d-dimensional hypercubes into sub-hypercubes are at least d-connected. Bounds on …
Note On Rainbow Connection In Oriented Graphs With Diameter 2, Rebecca Holliday, Colton Magnant, Pouria Salehi Nowbandegani
Note On Rainbow Connection In Oriented Graphs With Diameter 2, Rebecca Holliday, Colton Magnant, Pouria Salehi Nowbandegani
Theory and Applications of Graphs
In this note, we provide a sharp upper bound on the rainbow connection number of tournaments of diameter 2. For a tournament Τ of diameter 2, we show 2 ≤ → rc (Τ) ≤ 3. Furthermore, we provide a general upper bound on the rainbow κ-connection number of tournaments as a simple example of the probabilistic method. Finally, we show that an edge-colored tournament of κthdiameter 2 has rainbow κ-connection number at most approximately κ2.