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Total domination in plane triangulations
[article]

2020
*
arXiv
*
pre-print

A

arXiv:2011.04255v1
fatcat:n45cfivy7beoznvlv5obz5rm5u
*total**dominating*set of a graph G=(V,E) is a subset D of V such that every vertex*in*V is adjacent to at least one vertex*in*D. ... The*total**domination*number of G, denoted by γ _t (G), is the minimum cardinality of a*total**dominating*set of G. ... The upper bound 2n 5 on the*total**domination*number*in*near-*triangulations*is proved*in*Section 4. ...##
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Enumeration of Enumeration Algorithms
[article]

2016
*
arXiv
*
pre-print

*In*this paper, we enumerate enumeration problems and algorithms. This survey is under construction. If you know some results not

*in*this survey or there is anything wrong, please let me know. ... Comment A based

*plane*

*triangulation*is a

*plane*

*triangulation*with one designated edge on the outer face. ... Comment A based

*plane*

*triangulation*is a

*plane*

*triangulation*with one designated edge on the outer face. ...

##
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Dominating Plane Triangulations
[article]

2014
*
arXiv
*
pre-print

*In*1996, Tarjan and Matheson proved that if G is a

*plane*

*triangulated*disc with n vertices, γ (G)< n/3, where γ (G) denotes the

*domination*number of G. ...

*In*the present paper, it is proved that if G is a hamiltonian

*plane*

*triangulation*with |V(G)|=n vertices and minimum degree at least 4, then γ (G)<{ 2n/7, 5n/16}. ... Preferred Hamilton cycles

*in*

*plane*

*triangulations*Let G be a

*plane*

*triangulation*with δ(G) ≥ 4 and suppose G contains a Hamilton cycle H. ...

##
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Dominating maximal outerplane graphs and Hamiltonian plane triangulations
[article]

2019
*
arXiv
*
pre-print

Let $G$ be a graph and $\gamma (G)$ denote the

arXiv:1903.02462v1
fatcat:4ededjdiqzepnbhqywrjfeay5q
*domination*number of $G$, i.e. the cardinality of a smallest set of vertices $S$ such that every vertex of $G$ is either*in*$S$ or adjacent to a vertex*in*... by distance at least 3 on the boundary of $G$; and (2) a Hamiltonian*plane**triangulation*$G$ with $n \ge 23$ vertices has $\gamma (G)\le 5n/16 $. ... Introduction A*plane**triangulation*is a*plane*graph*in*which every face is bounded by a triangle. ...##
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Combinatorial bounds on connectivity for dominating sets in maximal outerplanar graphs

2016
*
Electronic Notes in Discrete Mathematics
*

*In*this article we study some variants of the

*domination*concept attending to the connectivity of the subgraph generated by the

*dominant*set. This study is restricted to maximal outerplanar graphs. ... We establish tight combinatorial bounds for connected

*domination*, semitotal

*domination*, independent

*domination*and weakly connected

*domination*for any n-vertex maximal outerplaner graph. ... A maximal outerplanar graph embedded

*in*the

*plane*corresponds to a

*triangulation*of a polygon. ...

##
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Efficient plane sweeping in parallel

1986
*
Proceedings of the second annual symposium on Computational geometry - SCG '86
*

We present techniques which result

doi:10.1145/10515.10539
dblp:conf/compgeom/AtallahG86
fatcat:dwk76wbmx5bzlewaut7z34vrty
*in*improved parallel algorithms for a number of problems whose efficient sequential algorithms use the*plane*-sweeping paradigm. ... The problems for which we give improved algorithms include intersection detection, trapezoidal decomposition,*triangulation*, and planar point location. ... (v)) are*totally*ordered. ...##
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Distance domination, guarding and vertex cover for maximal outerplanar graph
[article]

2013
*
arXiv
*
pre-print

This paper discusses a distance guarding concept on

arXiv:1307.2043v1
fatcat:ckc27lfdpfapzcsd5vpw2my3ee
*triangulation*graphs, which can be associated with distance*domination*and distance vertex cover. ... We show how these subjects are interconnected and provide tight bounds for any n-vertex maximal outerplanar graph: the 2d-guarding number, g_2d(n) = n/5; the 2d-distance*domination*number, gamma_2d(n) ... Such graph is called*triangulation*graph (*triangulation*, for short), because is the graph of a*triangulation*of a set of points*in*the*plane*(see Figures 1 and 2) . ...##
###
On Polyhedral Realization with Isosceles Triangles
[article]

2020
*
arXiv
*
pre-print

However, we also show that all Kleetopes of

arXiv:2009.00116v1
fatcat:gk6xwwvlsjbndjzapulsrntnha
*triangulated*polyhedral graphs have non-convex non-self-crossing realizations*in*which all faces are isosceles. ... We prove that the graphs of convex polyhedra with congruent isosceles faces have bounded diameter and have*dominating*sets of bounded size. ... angle, so the*total*angle is ≤ kπ + O(1), but*in*order to achieve*total*angular deficit at most 4π the*total*angle must be ≥ (2k − 4)π. ...##
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Dominating Sets in Planar Graphs

1996
*
European journal of combinatorics (Print)
*

Motivated by an application to unstructured multigrid calculations, we consider the problem of asymptotically minimizing the size of

doi:10.1006/eujc.1996.0048
fatcat:sncavh7rfvebzi2zwft3bfbwwa
*dominating*sets*in**triangulated*planar graphs. ... For*triangulated*discs we obtain a tight bound of = 1 3 . The upper bound proof yields a linear-time algorithm for nding an n=3 -size*dominating*set. ... Small*Dominating*Sets*in**Triangulated*Discs Our method for nding small*dominating*sets*in**triangulated*discs is based on a stronger result. ...##
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On Polyhedral Realization with Isosceles Triangles

2021
*
Graphs and Combinatorics
*

However, we also show that all Kleetopes of

doi:10.1007/s00373-021-02314-9
fatcat:vjzxpomrzvf2hh77kbhckfjogy
*triangulated*polyhedral graphs have non-convex non-self-crossing realizations*in*which all faces are isosceles. ... We prove that the graphs of convex polyhedra with congruent isosceles faces have bounded diameter and have*dominating*sets of bounded size. ... angle, so the*total*angle is kp þ Oð1Þ, but*in*order to achieve*total*angular deficit at most 4p the*total*angle must be ! ...##
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TRANSLATION QUERIES FOR SETS OF POLYGONS

1995
*
International journal of computational geometry and applications
*

Let S be a set of m polygons

doi:10.1142/s0218195995000131
fatcat:2gf3pv6n3vh4rh4v7stiqmkgxq
*in*the*plane*with a*total*of n vertices. ... A translation order for S*in*direction d is an order on the polygons such that no collisions occur if the polygons are moved one by one to infinity*in*direction d according to this order. ...*plane*. ...##
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Thoroughly Distributed Colorings
[article]

2016
*
arXiv
*
pre-print

Equivalently, every color is a

arXiv:1609.09684v1
fatcat:v7mi5bjirrhobpkxrnpkh3xhne
*total**dominating*set. We define (G) as the maximum number of colors*in*such a coloring and (G) as the fractional version thereof. ... We also consider the related concepts*in*hypergraphs. ...*In*order to*totally**dominate*the new vertices added*in*each face of the base graph G, all*total**dominating*sets of T (G) contain at least two vertices of G. ...##
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Dominating sets in triangulations on surfaces

2011
*
Ars Mathematica Contemporanea
*

A

doi:10.26493/1855-3974.200.fbe
fatcat:iwso2q7t7fakresvv54puhepwe
*dominating*set D ⊆ V (G) of a graph G is a set such that each vertex v ∈ V (G) is either*in*the set or adjacent to a vertex*in*the set. ... Matheson and Tarjan (1996) proved that any n-vertex*plane**triangulation*has a*dominating*set of size at most n/3, and conjectured a bound of n/4 for n sufficiently large. ... We would also like to thank the referees for their careful work, which led to critical improvements*in*the paper. ...##
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Triangulations and soliton graphs for totally positive Grassmannian
[article]

2018
*
arXiv
*
pre-print

For the positive Grassmannian Gr(2,M)_>0, Kodama and Williams showed that soliton graphs are

arXiv:1808.01587v1
fatcat:6rte2zlpybhhvki4zrovoie2we
*in*bijection with*triangulations*of the M-gon. ... It is well known that regular soliton solutions of the KP equation may be constructed from points*in*the*totally*nonnegative Grassmannian Gr(N,M)_≥ 0. ... That is, f M(A) (x, y, t) represents a*dominant**plane*z = Θ I (x, y, t)*in*R 3 for fixed t. ...##
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Dominating Sets in Plane Triangulations
[article]

2010
*
arXiv
*
pre-print

*In*1996, Matheson and Tarjan conjectured that any n-vertex

*triangulation*with n sufficiently large has a

*dominating*set of size at most n/4. We prove this for graphs of maximum degree 6. ... For any closed walk W

*in*the

*plane*dual of G ′ , let h(W ) be the

*total*number of such vertices for all cycles

*in*W . ... A

*triangulation*is a

*plane*graph

*in*which every face is a 3-face. A triangle is a subgraph isomorphic to K 3 . ...

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