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Pairs of trees in tree–tree triangulations
2007
Discrete Mathematics
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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. ...
doi:10.1016/j.disc.2005.11.087
fatcat:fhgddb23krfwzg2tbpstriwvau
On the Representation of Triangulated Graphs in Trees
1984
European journal of combinatorics (Print)
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The intersection graph of a family of subtrees of a 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. ...
doi:10.1016/s0195-6698(84)80014-1
fatcat:up6iw53mxbgd5pprf5l7lgixve
Common Edges in Rooted Trees and Polygonal Triangulations
2013
Electronic Journal of Combinatorics
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Rotation distance between rooted binary 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. ...
doi:10.37236/2541
fatcat:ll5tgudgurbnvaasyjnohzdl3q
Triangulated edge intersection graphs of paths in a tree
1985
Discrete Mathematics
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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. ...
doi:10.1016/0012-365x(85)90050-0
fatcat:viu3xmfqszdzpk3bligu3pif5a
Trees and spatial topology change in causal dynamical triangulations
2013
Journal of Physics A: Mathematical and Theoretical
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Generalized causal dynamical 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] . ...
doi:10.1088/1751-8113/46/31/315201
fatcat:f7ogffsac5cyrjuitmpy55eea4
Computation of Chromatic Polynomials Using Triangulations and Clique Trees
[chapter]
2005
Lecture Notes in Computer Science
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To achieve our goal, we use the properties of 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. ...
doi:10.1007/11604686_32
fatcat:s6ea76zshjcq3a6txx4bivs2gq
A criterion for sharpness in tree enumeration and the asymptotic number of triangulations in Kuperberg's G2 spider
[article]
2020
arXiv
pre-print
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2020 pre-print arXiv:2003.07984v1 fatcat:fgh2k5qf2ja3ldb7zquypv63zy
Kuperberg proved 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. ...
arXiv:2003.07984v2
fatcat:lvfpkftgojdg5jm7uquviusy6i
Common edges in rooted trees and polygonal triangulations
2013
unpublished
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Rotation distance between rooted binary 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. ...
fatcat:r5njbpuo7zbe7nwb4fh3uovldm
Convex polygon triangulation based on planted trivalent binary tree and ballot problem
2019
Turkish Journal of Electrical Engineering and Computer Sciences
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The properties of the Catalan numbers were examined and their decomposition and application 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. ...
doi:10.3906/elk-1805-143
fatcat:5smgwt6jjrbc3osrfvj4is7k64
A Simple Linear Time Algorithm for Triangulating Three-Colored Graphs
1993
Journal of Algorithms
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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. ...
doi:10.1006/jagm.1993.1035
fatcat:yj7hwa6kz5a35kzdur5rzi4tom
A simple linear time algorithm for triangulating three-colored graphs
[chapter]
1992
Lecture Notes in Computer Science
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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. ...
doi:10.1007/3-540-55210-3_201
fatcat:b5o5a3bdkjbdtncj7vecrvfpsa
JAVA Implementation for Triangulation of Convex Polygon Based on Lukasiewicz's Algorithm and Binary Trees
2013
Southeast Europe Journal of Soft Computing
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The notation that is obtained is expressed 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. ...
doi:10.21533/scjournal.v2i2.26
fatcat:3h7lxs7bgfcmrkie3vhs3m3cda
Triangulations without pointed spanning trees
2008
Computational geometry
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Problem 50 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. ...
doi:10.1016/j.comgeo.2007.07.006
fatcat:qomntjn5v5ez7lx4x4kz7zgc2e
Hamiltonian-connectedness of triangulations with few separating triangles
[article]
2016
arXiv
pre-print
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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] . ...
arXiv:1605.01231v1
fatcat:6pa7ddpe5vau7p5om5rdcj4vm4
Diagonal-Flip Distance Algorithms of Three Type Triangulations
2008
2008 International Conference on Computer Science and Software Engineering
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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 ). ...
doi:10.1109/csse.2008.337
dblp:conf/csse/WangWLZ08c
fatcat:ffd7ri3isvdrra4yr3t7silori
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