scholarly journals On Colored Edge Cuts in Graphs

2018 ◽  
Author(s):  
Luerbio Faria ◽  
Sulamita Klein ◽  
Ignasi Sau ◽  
Uéverton S. Souza ◽  
Rubens Sucupira
Keyword(s):  
Parameterized Complexity ◽  
Colored Graphs ◽  
Colored Edge

In this work we present some results on the classical and parameterized complexity of finding cuts in edge-colored graphs. In general, we are interested in problems of finding cuts {A,B} which minimize or maximize the number of colors occurring in the edges with exactly one endpoint in A.  

scholarly journals Indirect identification of horizontal gene transfer

2021 ◽  
Vol 83 (1) ◽  
Author(s):  
David Schaller ◽  
Manuel Lafond ◽  
Peter F. Stadler ◽  
Nicolas Wieseke ◽  
Marc Hellmuth
Keyword(s):  
Gene Transfer ◽  
Horizontal Gene Transfer ◽  
Polynomial Time ◽  
Divergence Time ◽  
Recognition Algorithm ◽  
Vertex Coloring ◽  
Implicit Methods ◽  
Colored Graphs ◽  
Wide Range ◽  
Complete Multipartite

AbstractSeveral implicit methods to infer horizontal gene transfer (HGT) focus on pairs of genes that have diverged only after the divergence of the two species in which the genes reside. This situation defines the edge set of a graph, the later-divergence-time (LDT) graph, whose vertices correspond to genes colored by their species. We investigate these graphs in the setting of relaxed scenarios, i.e., evolutionary scenarios that encompass all commonly used variants of duplication-transfer-loss scenarios in the literature. We characterize LDT graphs as a subclass of properly vertex-colored cographs, and provide a polynomial-time recognition algorithm as well as an algorithm to construct a relaxed scenario that explains a given LDT. An edge in an LDT graph implies that the two corresponding genes are separated by at least one HGT event. The converse is not true, however. We show that the complete xenology relation is described by an rs-Fitch graph, i.e., a complete multipartite graph satisfying constraints on the vertex coloring. This class of vertex-colored graphs is also recognizable in polynomial time. We finally address the question “how much information about all HGT events is contained in LDT graphs” with the help of simulations of evolutionary scenarios with a wide range of duplication, loss, and HGT events. In particular, we show that a simple greedy graph editing scheme can be used to efficiently detect HGT events that are implicitly contained in LDT graphs.

scholarly journals Path homology theory of edge-colored graphs

2021 ◽  
Vol 19 (1) ◽  
pp. 706-723
Author(s):  
Yuri V. Muranov ◽  
Anna Szczepkowska
Keyword(s):  
Spectral Sequence ◽  
Edge Coloring ◽  
Homology Theory ◽  
Homotopy Category ◽  
Homology Groups ◽  
Colored Graphs ◽  
Natural Filtration ◽  
Definition Of ◽  
Exact Sequences

Abstract In this paper, we introduce the category and the homotopy category of edge-colored digraphs and construct the functorial homology theory on the foundation of the path homology theory provided by Grigoryan, Muranov, and Shing-Tung Yau. We give the construction of the path homology theory for edge-colored graphs that follows immediately from the consideration of natural functor from the category of graphs to the subcategory of symmetrical digraphs. We describe the natural filtration of path homology groups of any digraph equipped with edge coloring, provide the definition of the corresponding spectral sequence, and obtain commutative diagrams and braids of exact sequences.

Parameterized complexity of fair feedback vertex set problem

2021 ◽  
Vol 867 ◽  
pp. 1-12
Author(s):  
Lawqueen Kanesh ◽  
Soumen Maity ◽  
Komal Muluk ◽  
Saket Saurabh
Keyword(s):  
Parameterized Complexity ◽  
Feedback Vertex Set ◽  
Vertex Set ◽  
Feedback Vertex Set Problem

A compendium of parameterized complexity results

1994 ◽  
Vol 25 (3) ◽  
pp. 122-123 ◽  
Author(s):  
Michael T. Hallett ◽  
H. Todd Wareham
Keyword(s):  
Parameterized Complexity ◽  
Complexity Results

scholarly journals Revisiting the parameterized complexity of Maximum-Duo Preservation String Mapping

2020 ◽  
Vol 847 ◽  
pp. 27-38
Author(s):  
Christian Komusiewicz ◽  
Mateus de Oliveira Oliveira ◽  
Meirav Zehavi
Keyword(s):  
Parameterized Complexity

The Book Review Column1

2021 ◽  
Vol 51 (4) ◽  
pp. 4-5
Author(s):  
Frederic Green
Keyword(s):  
Parameterized Complexity ◽  
Property Testing ◽  
The Third ◽  
Geometric Problems ◽  
The Subject

The three books reviewed in this column are about central ideas in algorithms, complexity, and geometry. The third one brings together topics from the first two by applying techniques of both property testing (the subject of the first book) and parameterized complexity (including its more focused incarnation studied in the second book, kernelization) to geometric problems.

scholarly journals The Action of the Weyl Group on the $$E_8$$ Root System

2021 ◽  
Author(s):  
Rosa Winter ◽  
Ronald van Luijk
Keyword(s):  
Automorphism Group ◽  
Weyl Group ◽  
Root System ◽  
Sufficient Conditions ◽  
Maximal Clique ◽  
Necessary And Sufficient Conditions ◽  
Inner Product ◽  
Colored Graphs ◽  
Necessary And Sufficient ◽  
Root Polytope

AbstractLet $$\varGamma $$ Γ be the graph on the roots of the $$E_8$$ E 8 root system, where any two distinct vertices e and f are connected by an edge with color equal to the inner product of e and f. For any set c of colors, let $$\varGamma _c$$ Γ c be the subgraph of $$\varGamma $$ Γ consisting of all the 240 vertices, and all the edges whose color lies in c. We consider cliques, i.e., complete subgraphs, of $$\varGamma $$ Γ that are either monochromatic, or of size at most 3, or a maximal clique in $$\varGamma _c$$ Γ c for some color set c, or whose vertices are the vertices of a face of the $$E_8$$ E 8 root polytope. We prove that, apart from two exceptions, two such cliques are conjugate under the automorphism group of $$\varGamma $$ Γ if and only if they are isomorphic as colored graphs. Moreover, for an isomorphism f from one such clique K to another, we give necessary and sufficient conditions for f to extend to an automorphism of $$\varGamma $$ Γ , in terms of the restrictions of f to certain special subgraphs of K of size at most 7.

Sign in / Sign up

Export Citation Format

Share Document