Improved Feedback Vertex Sets in Kautz Digraphs K (d, n)

2014 ◽  
Author(s):  
Xirong Xu ◽  
Chun Yin ◽  
Sijia Zhang ◽  
Yazhen Huang
Keyword(s):  
Kautz Digraphs ◽  
Vertex Sets

scholarly journals Distance domination of generalized de Bruijn and Kautz digraphs

2016 ◽  
Vol 12 (2) ◽  
pp. 339-357
Author(s):  
Yanxia Dong ◽  
Erfang Shan ◽  
Xiao Min
Keyword(s):  
Kautz Digraphs ◽  
De Bruijn ◽  
Distance Domination

scholarly journals Approximating minimum feedback vertex sets in hypergraphs

2000 ◽  
Vol 246 (1-2) ◽  
pp. 107-116 ◽  
Author(s):  
Toshihiro Fujito
Keyword(s):  
Vertex Sets

Analysis of Critical and Redundant Vertices in Controlling Directed Complex Networks Using Feedback Vertex Sets

2018 ◽  
Vol 25 (10) ◽  
pp. 1071-1090 ◽  
Author(s):  
Yu Bao ◽  
Morihiro Hayashida ◽  
Pengyu Liu ◽  
Masayuki Ishitsuka ◽  
Jose C. Nacher ◽  
...  
Keyword(s):  
Complex Networks ◽  
Vertex Sets

scholarly journals Topological Infinite Gammoids, and a New Menger-Type Theorem for Infinite Graphs

10.37236/6083 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Johannes Carmesin
Keyword(s):  
Type Theorem ◽  
Main Tool ◽  
Infinite Graphs ◽  
Disjoint Paths ◽  
Natural Topology ◽  
Locally Finite ◽  
Finite Graphs ◽  
Locally Finite Graphs ◽  
Vertex Sets ◽  
Special Case

Answering a question of Diestel, we develop a topological notion of gammoids in infinite graphs which, unlike traditional infinite gammoids, always define a matroid.As our main tool, we prove for any infinite graph $G$ with vertex-sets $A$ and $B$, if every finite subset of $A$ is linked to $B$ by disjoint paths, then the whole of $A$ can be linked to the closure of $B$ by disjoint paths or rays in a natural topology on $G$ and its ends.This latter theorem implies the topological Menger theorem of Diestel for locally finite graphs. It also implies a special case of the infinite Menger theorem of Aharoni and Berger.

MINIMUM WEIGHT FEEDBACK VERTEX SETS IN CIRCLE n-GON GRAPHS AND CIRCLE TRAPEZOID GRAPHS

2011 ◽  
Vol 03 (03) ◽  
pp. 323-336 ◽  
Author(s):  
FANICA GAVRIL
Keyword(s):  
Minimum Weight ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Circle Graphs ◽  
Intersection Model ◽  
The Family ◽  
Positive Weights ◽  
Vertex Set ◽  
Vertex Sets ◽  
Trapezoid Graphs

A circle n-gon is the region between n or fewer non-crossing chords of a circle, no chord connecting the arcs between two other chords; the sides of a circle n-gon are either chords or arcs of the circle. A circle n-gon graph is the intersection graph of a family of circle n-gons in a circle. The family of circle trapezoid graphs is exactly the family of circle 2-gon graphs and the family of circle graphs is exactly the family of circle 1-gon graphs. The family of circle n-gon graphs contains the polygon-circle graphs which have an intersection representation by circle polygons, each polygon with at most n chords. We describe a polynomial time algorithm to find a minimum weight feedback vertex set, or equivalently, a maximum weight induced forest, in a circle n-gon graph with positive weights, when its intersection model by n-gon-interval-filaments is given.

scholarly journals Limit theorems for isotropic random walks on triangle buildings

2002 ◽  
Vol 73 (3) ◽  
pp. 301-334 ◽  
Author(s):  
Marc Lindlbauer ◽  
Michael Voit
Keyword(s):  
Limit Theorem ◽  
Random Walks ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Two Dimensional ◽  
Littlewood Polynomials ◽  
Large Numbers ◽  
Moment Functions ◽  
Vertex Sets ◽  
Isotropic Random

AbstractThe spherical functions of triangle buildings can be described in terms of certain two-dimensional orthogonal polynomials on Steiner's hypocycloid which are closely related to Hall-Littlewood polynomials. They lead to a one-parameter family of two-dimensional polynimial hypergroups. In this paper we investigate isotropic random walks on the vertex sets of triangle buildings in terms of their projections to these hypergroups. We present strong laws of large numbers, a central limit theorem, and a local limit theorem; all these results are well-known for homogeneous trees. Proofs are based on moment functions on hypergroups and on explicit expansions of the hypergroup characters in terms of certain two-dimensional Tchebychev polynimials.

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