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Pairs of trees in tree–tree triangulations

2007
*
Discrete Mathematics
*

*In*particular, for a pair made up of any

*tree*and any long enough path, there is a spherical

*triangulation*whose graph is partitionable into that pair. ... Hence each

*tree*-

*tree*

*triangulation*is a

*triangulation*of the 2-sphere. Recognizing

*tree*-

*tree*

*triangulations*among all simple spherical ones can be seen to be an NP-complete problem. ...

*In*other words, the graph of a 0 -1

*triangulation*admits of a bipartition into

*trees*isomorphic to 0 and 1 . It is easily seen that each

*tree*-

*tree*

*triangulation*T is spherical. ...

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On the Representation of Triangulated Graphs in Trees

1984
*
European journal of combinatorics (Print)
*

The intersection graph of a family of subtrees of a

doi:10.1016/s0195-6698(84)80014-1
fatcat:up6iw53mxbgd5pprf5l7lgixve
*tree*is always a*triangulated*graph, and vice versa every finite*triangulated*graph can be represented*in*this way. ... The analogous statement is*in*general not true for infinite*triangulated*graphs. ...*In*the present note the same problem is treated if the hypothesis that G be finite is omitted. We shall see that*in*general an infinite*triangulated*graph is not*tree*-representable. ...##
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Common Edges in Rooted Trees and Polygonal Triangulations

2013
*
Electronic Journal of Combinatorics
*

Rotation distance between rooted binary

doi:10.37236/2541
fatcat:ll5tgudgurbnvaasyjnohzdl3q
*trees*measures the degree of similarity of two*trees*with ordered leaves and is equivalent to edge-flip distance between triangular subdivisions of regular polygons ... Here we describe the distribution of common edges between randomly-selected*triangulations*and measure the sizes of the remaining pieces into which the common edges separate the polygons. ... Thus, a*triangulation*of size n means a*triangulation*on an n + 1-gon or with n leaves*in*the underlying binary*tree*. ...##
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Triangulated edge intersection graphs of paths in a tree

1985
*
Discrete Mathematics
*

*in*T, and G is called an edge intersection graph of paths

*in*a

*tree*(EPT graph) if G = O(E(T), 9) for some path collection 9

*in*a

*tree*T. ... A graph G is a vertex intersection graph of paths

*in*a

*tree*(shortly, VPT graph) if G = f2( V(T), 9) for a certain

*tree*T and a path collection 9? ...

*in*T, and G is called an edge intersection graph of paths

*in*a

*tree*(EPT graph) if G = O(E(T), 9) for some path collection 9

*in*a

*tree*T. ...

##
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Trees and spatial topology change in causal dynamical triangulations

2013
*
Journal of Physics A: Mathematical and Theoretical
*

Generalized causal dynamical

doi:10.1088/1751-8113/46/31/315201
fatcat:f7ogffsac5cyrjuitmpy55eea4
*triangulations*(generalized CDT) is a model of two-dimensional quantum gravity*in*which a limited number of spatial topology changes is allowed to occur. ... We solve the model at the discretized level using bijections between quadrangulations and*trees*. ... Causal*triangulations*A similar bijection between causal*triangulations*and*trees*has been used*in*[36, 32, 27] and earlier*in*a slightly different form*in*[26] . ...##
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Computation of Chromatic Polynomials Using Triangulations and Clique Trees
[chapter]

2005
*
Lecture Notes in Computer Science
*

To achieve our goal, we use the properties of

doi:10.1007/11604686_32
fatcat:s6ea76zshjcq3a6txx4bivs2gq
*triangulations*and clique-*trees*with respect to the previous operations, and guide our algorithm to efficiently divide the original problem. ...*In*this paper, we present a new algorithm for computing the chromatic polynomial of a general graph G. ...*Triangulation*and clique*trees*A chordal graph G is a graph*in*which there are no induced cycles of length > 3. ...##
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A criterion for sharpness in tree enumeration and the asymptotic number of triangulations in Kuperberg's G2 spider
[article]

2020
*
arXiv
*
pre-print

Kuperberg proved

arXiv:2003.07984v2
fatcat:lvfpkftgojdg5jm7uquviusy6i
*in*that this identity holds*in*the case that b_n=Inv_G_2 (V(λ_1)^⊗ n), where V(λ_1) is the 7-dimensional fundamental representation of G_2, and a_n is the number of*triangulations*of a ... Given a non-negative sequence (a_n)_n≥ 1, the identity B(x)=A(xB(x)) for generating functions A(x)=1+∑_n≥ 1 a_n x^n and B(x)=1+∑_n≥ 1 b_n x^n determines the number b_n of rooted planar*trees*with n vertices ... The author is also grateful to Greg Kuperberg for his encouragement and for several helpful discussions about various aspects of the subject matter*in*this paper. ...##
###
Common edges in rooted trees and polygonal triangulations

2013
unpublished

Rotation distance between rooted binary

fatcat:r5njbpuo7zbe7nwb4fh3uovldm
*trees*measures the degree of similarity of two*trees*with ordered leaves and is equivalent to edge-flip distance between triangular subdivisions of regular polygons ... Here we describe the distribution of common edges between randomly-selected*triangulations*and measure the sizes of the remaining pieces into which the common edges separate the polygons. ... Thus, a*triangulation*of size n means a*triangulation*on an n + 1-gon or with n leaves*in*the underlying binary*tree*. ...##
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Convex polygon triangulation based on planted trivalent binary tree and ballot problem

2019
*
Turkish Journal of Electrical Engineering and Computer Sciences
*

The properties of the Catalan numbers were examined and their decomposition and application

doi:10.3906/elk-1805-143
fatcat:5smgwt6jjrbc3osrfvj4is7k64
*in*developing the hierarchy and*triangulation**trees*were analyzed. ... This paper presents a new technique of generation of convex polygon*triangulation*based on planted trivalent binary*tree*and ballot notation. ...*Tree*of*triangulations*and expression of the Catalan numbers The first step*in*our method is generating a complete*triangulation**tree*from the initial basic triangle to the given n -gon. ...##
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A Simple Linear Time Algorithm for Triangulating Three-Colored Graphs

1993
*
Journal of Algorithms
*

*In*this paper we consider the problem of determining whether a given colored graph can be

*triangulated*, such that no edges between vertices of the same color are added. ...

*In*this paper we give a simple linear time algorithm that solves the problem when there are three colors. ... We must show that G is a

*tree*of cycles. Consider a

*triangulation*of G into a 2-

*tree*H. Consider the edges

*in*H that are not

*in*G. ...

##
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A simple linear time algorithm for triangulating three-colored graphs
[chapter]

1992
*
Lecture Notes in Computer Science
*

*In*this paper we consider the problem of determining whether a given colored graph can be

*triangulated*, such that no edges between vertices of the same color are added. ...

*In*this paper we give a simple linear time algorithm that solves the problem when there are three colors. ... We must show that G is a

*tree*of cycles. Consider a

*triangulation*of G into a 2-

*tree*H. Consider the edges

*in*H that are not

*in*G. ...

##
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JAVA Implementation for Triangulation of Convex Polygon Based on Lukasiewicz's Algorithm and Binary Trees

2013
*
Southeast Europe Journal of Soft Computing
*

The notation that is obtained is expressed

doi:10.21533/scjournal.v2i2.26
fatcat:3h7lxs7bgfcmrkie3vhs3m3cda
*in*the form of binary records. A presented method of*triangulations*is based on Lukasiewicz's algorithm and binary*trees*. ...*Triangulation*of the polygon is one of the fundamental algorithm computational geometry. This paper describes one method*triangulations*of a convex polygon. ...*In*paper is described graph of*triangulations*of a convex polygon and*tree*of*triangulations*, while the authors of the paper (Devroye, 1999) of random*triangulations*and*trees*. ...##
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Triangulations without pointed spanning trees

2008
*
Computational geometry
*

Problem 50

doi:10.1016/j.comgeo.2007.07.006
fatcat:qomntjn5v5ez7lx4x4kz7zgc2e
*in*the Open Problems Project of the computational geometry community asks whether any*triangulation*on a point set*in*the plane contains a pointed spanning*tree*as a subgraph. ... As a consequence we show that there exist*triangulations*which require a linear number of edge flips to become Hamiltonian. ... Acknowledgements The innocent looking conjecture that any*triangulation*contains a pointed spanning*tree*as a subgraph has fascinated several people. ...##
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Hamiltonian-connectedness of triangulations with few separating triangles
[article]

2016
*
arXiv
*
pre-print

*In*order to show bounds on the strongest form of this theorem, we proved that for any s≥4 there are 3-connected

*triangulation*with s separating triangles that are not hamiltonian-connected. ... We prove that 3-connected

*triangulations*with at most one separating triangle are hamiltonian-connected. ... The author would also like to thank Jasper Souffriau for providing him with the programs to determine the decomposition

*tree*of a

*triangulation*which were developed for [1] . ...

##
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Diagonal-Flip Distance Algorithms of Three Type Triangulations

2008
*
2008 International Conference on Computer Science and Software Engineering
*

*In*this paper we study the diagonal flipping problem

*in*three special type

*triangulations*of Ò (Ò ) vertex convex polygons (and rotations

*in*three type binary

*trees*). ...

*trees*). ... A rotation

*in*a binary

*tree*is a local restructuring of the

*tree*that changes the position of an internal node and one of its children while the symmetric order

*in*the

*tree*is preserved (see Fig.1 ). ...

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