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296
Subdivision Tree Representation of Arbitrary Triangle Meshes
, 1998
"... We investigate a new way to represent arbitrary triangle meshes. We prove that a large class of triangle meshes, called normal triangle meshes, can be represented by a subdivision tree, where each subdivision is one of four elementary subdivision types. We also show how to partition an arbitrary tri ..."
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Cited by 1 (1 self)
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We investigate a new way to represent arbitrary triangle meshes. We prove that a large class of triangle meshes, called normal triangle meshes, can be represented by a subdivision tree, where each subdivision is one of four elementary subdivision types. We also show how to partition an arbitrary
Subdivision Tree Representation of Arbitrary Triangle Meshes
, 1998
"... We investigate a new way to represent arbitrary triangle meshes. We prove that a large class of triangle meshes, called normal triangle meshes, can be represented by a subdivision tree, where each subdivision is one of four elementary subdivision types. We also show how to partition an arbitrary tri ..."
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We investigate a new way to represent arbitrary triangle meshes. We prove that a large class of triangle meshes, called normal triangle meshes, can be represented by a subdivision tree, where each subdivision is one of four elementary subdivision types. We also show how to partition an arbitrary
Lossless Topological Subdivision of Triangle Meshes
, 1999
"... In this paper, we investigate subdivision tree representations of arbitrary triangle meshes. By subdivision, we mean the recursive topological partitioning of a triangle into subtriangles. Such a process can be represented by a subdivision tree. We identify the class of regular triangle meshes, t ..."
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In this paper, we investigate subdivision tree representations of arbitrary triangle meshes. By subdivision, we mean the recursive topological partitioning of a triangle into subtriangles. Such a process can be represented by a subdivision tree. We identify the class of regular triangle meshes
On the domination subdivision numbers of trees
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 46 (2010), PAGES 233–239
, 2010
"... A set D of vertices of a graph G is a dominating set if every vertex in V \ D is adjacent to some vertex in D. The domination number γ(G) of G is the minimum cardinality of a dominating set of G. The domination subdivision number of G is the minimum number of edges that must be subdivided (where eac ..."
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each edge in G can be subdivided at most once) in order to increase the domination number. Arumugam has shown that for any tree, the domination subdivision number always lies between one and three inclusive. In this paper, we provide a constructive characterization of trees whose domination subdivision
SUBDIVISION OF COMPLEXES OF kTREES
, 2005
"... Abstract. Let Π (k) be the poset of partitions of {1,2,..., (n − 1)k + 1} with (n−1)k+1 block sizes congruent to 1 modulo k. We prove that the order complex ∆(Π (k) (n−1)k+1) is a subdivision of the complex of ktrees T k n, thereby answering a question posed by Feichtner [F, 5.2]. The result is obt ..."
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Abstract. Let Π (k) be the poset of partitions of {1,2,..., (n − 1)k + 1} with (n−1)k+1 block sizes congruent to 1 modulo k. We prove that the order complex ∆(Π (k) (n−1)k+1) is a subdivision of the complex of ktrees T k n, thereby answering a question posed by Feichtner [F, 5.2]. The result
Planar Point Location Using Persistent Search Trees
, 1986
"... A classical problem in computational geometry is the planar point location problem. This problem calls for preprocessing a polygonal subdivision of the plane defined by n line segments so that, given a sequence of points, the polygon containing each point can be determined quickly online. Several ..."
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Cited by 177 (4 self)
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A classical problem in computational geometry is the planar point location problem. This problem calls for preprocessing a polygonal subdivision of the plane defined by n line segments so that, given a sequence of points, the polygon containing each point can be determined quickly on
Trees with domination subdivision number one
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 42 (2008), PAGES 201–209
, 2008
"... The domination subdivision number sdγ(G) of a graph G is the minimum number of edges that must be subdivided to increase the domination number of G. We present a simple characterization of trees with sdγ =1 and a fast algorithm to determine whether a tree has this property. ..."
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Cited by 2 (0 self)
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The domination subdivision number sdγ(G) of a graph G is the minimum number of edges that must be subdivided to increase the domination number of G. We present a simple characterization of trees with sdγ =1 and a fast algorithm to determine whether a tree has this property.
On Pathos Lict Subdivision of a Tree
"... Abstract: Let G be a graph and E1 ⊂ E(G). A Smarandachely E1lict graph nE1(G) of a graph G is the graph whose point set is the union of the set of lines in E1 and the set of cutpoints of G in which two points are adjacent if and only if the corresponding lines of G are adjacent or the corresponding ..."
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is concentrated only on trees. We present a characterization of those graphs, whose lict subdivision graph is planar, outerplanar, maximal outerplanar and minimally nonouterplanar. Further, we also establish the characterization for Pn[S(T)] to be eulerian and hamiltonian. Key Words: pathos, path number
Trees whose domination subdivision number is one
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 40 (2008), PAGES 161–166
, 2008
"... A set S of vertices of a graph G = (V, E) is a dominating set if every vertex of V (G)\S is adjacent to some vertex in S. The domination number γ(G) is the minimum cardinality of a dominating set of G. The domination subdivision number sdγ(G) is the minimum number of edges that must be subdivided (e ..."
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Cited by 1 (0 self)
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, in their paper entitled “Trees with domination subdivision number three,” gave two characterizations of trees whose domination subdivision number is three. In this paper we characterize all trees whose domination subdivision number is one.
Strong weakly connected domination subdivisible graphs
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 47 (2010), PAGES 269–277
, 2010
"... The weakly connected domination subdivision number sdγw(G) ofaconnected graph G is the minimum number of edges which must be subdivided (where each edge can be subdivided at most once) in order to increase the weakly connected domination number. The graph is strongγ wsubdivisible if for each edge u ..."
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all strongγw1subdivisible and strongγw2subdivisible trees and give some properties of strongγwksubdivisible graphs for k =1, 2.
Results 1  10
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296