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Adjacent vertices on the b-matching polyhedron

1981
*
Discrete Mathematics
*

Therelfore we ch:iracterize here

doi:10.1016/0012-365x(81)90256-9
fatcat:rfdvb7hdfvcc3fazqbiz7mjcie
*the**adjacency**on**the*i?-*matching**polyhedron*by*the*sID-called coloring crirei,ion, a very general*adjacency*criterion developed in [<I]. ...*The**adjacency**on**the*convex hull of*the*inlzidence vectors of*the**b*-*matchings*is characterized by a very general*adjacency*criterion,*the*coloring triter*on*, which is at least sufficient for all O-l-polyhedra ... Let G = (V, E) be a graph with n*vertices*and*b*EN;~. 7hen*the**adjacency*of two*b*-*matchings*of G*on**the**b*-*matching*polyhtrdron of G can be checked by*the*coloring algorithm with time and space complexity ...##
###
Adjacency on combinatorial polyhedra

1995
*
Discrete Applied Mathematics
*

We consider a path

doi:10.1016/0166-218x(94)00092-r
fatcat:odmniuhyezbzhghqp2ullqlftm
*on**the**polyhedron*satisfying*the*condition that for each co-ordinate,*the**vertices*in a path form a monotonic sequence. ... When*one*of*the*end*vertices*of*the*path is optimal to an optimization problem defined*on**the**polyhedron*,*the*associated objective values form a monotonic sequence and*the*length of*the*path is bounded ...*Adjacency**on*combinatorial polyhedra We will begin this section by considering a*polyhedron*P G R" satisfying Property*B*. And we shall add Property A later. ...##
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Page 4665 of Mathematical Reviews Vol. , Issue 80M
[page]

1980
*
Mathematical Reviews
*

Harary (Cambridge)
Hausmann, Dirk 80m:05094 Complexity of

*the*testing of*adjacency**on**the**b*-*matching**polyhedron*. Third Symposium*on*Operations Research (Univ. ...*B*18 (1975), 138-154; MR 51 #7949] of*the**adjacency*of two*matchings*is extended to*b*-*matchings*: two*b*-*matchings*F,, F, of G are*adjacent*if*the*points u(F;), u( F,) belong to*the*same edge of*the**b*-*matching*...##
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Hamiltonicity and combinatorial polyhedra

1981
*
Journal of combinatorial theory. Series B (Print)
*

We say that a

doi:10.1016/0095-8956(81)90032-0
fatcat:sc5ozzhe7jay7ofeagiifhasde
*polyhedron*with O-1 valued*vertices*is combinatorial if*the*midpoint of*the*line joining any pair of nonadjacent*vertices*is*the*midpoint of*the*line joining another pair of*vertices*. ... We show*the*graph of a combinatorial*polyhedron*is always either a hypercube (i.e., isomorphic to*the*convex hull of a k-dimension unit cube) or else is hamilton connected (every pair of nodes is*the*set ... Since two*vertices*of a*polyhedron*are*adjacent*if and only if they are*the**vertices*of a*one*dimensional face, we see that (2. 2) U, u E X are*adjacent*nodes of G(X) if and only if, for every Iz satisfying ...##
###
Hamiltonicity in (0–1)-polyhedra

1984
*
Journal of combinatorial theory. Series B (Print)
*

*The*graph G(P) of a

*polyhedron*P has a node corresponding to each vertex of P and two nodes are

*adjacent*in G(P) if and only if

*the*corresponding

*vertices*of P are

*adjacent*

*on*P. ... has (0-1)valued

*vertices*and is of dimension d (<n) then there exists a

*polyhedron*P' g IRd having (0-1)valued

*vertices*such that G(P) 1 G(P'). ... Two

*vertices*are

*adjacent*if and only if

*the*symmetric difference of

*the*corresponding

*matchings*consists of a single alternating cycle. ...

##
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The zipper foldings of the diamond

2015
*
Involve. A Journal of Mathematics
*

In our foldings, all polyhedra will have at most 6

doi:10.2140/involve.2015.8.521
fatcat:zwv242hca5a57n26yif2rm3oge
*vertices*, resulting from gluing A,*B*, C, and D to some other point*on**the*perimeter, as well as*the**vertices*S and E, which each glue to themselves. ... They vary*the*length of this edge until*the*dihedral angles of*the*faces incident to*the*edge*match*. We utilize a different method that also reduces a partial*polyhedron*to*one*parameter of change. ...##
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Characterizations of adjacency on the branching polyhedron

1979
*
Discrete Mathematics
*

Given two distinct branchings of a directed graph G, we present several conditions which are equivalent to

doi:10.1016/0012-365x(79)90027-x
fatcat:tdshoebjejdihnq3lyijxdooqm
*the*corresporiding incidence vectors of*the*branchings being*adjacent**on**the*branching*polyhedron*...*The*proof of these equivalences uses a "shrinking algorithm'* whi_h will determine in O(n') time and space whether or not*the*incidence vectors are*adjacent*. ... In his thesis [7]*one*of*the*authors developed a very general criterion for*the**adjacency*of two*vertices*of a O-l*polyhedron*. ...##
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Pancyclic properties of the graph of some 0–1 polyhedra

1984
*
Journal of combinatorial theory. Series B (Print)
*

In this paper it is shown that a certain class of (&l) polyhedra, which includes

doi:10.1016/0095-8956(84)90040-6
fatcat:p5zqiqu7efei7i4y6fiwjf2v44
*the*matroid basis polytopes and*the*perfect*matching*polytopes, have graphs with*the*property that*the*edges, under a certain ... condition, belong to cycles of every length I > 3, and*the*others to cycles of every length I ) 4. ... Thanks to*one*of*the*referees for*the*careful reading of*the*manuscript and*the*many suggestions he made. ...##
###
Filling gaps in the boundary of a polyhedron

1995
*
Computer Aided Geometric Design
*

*The*algorithm uses a partial curve

*matching*technique for

*matching*parts of

*the*defects, and an optimal triangulation of 3-D polygons for resolving

*the*unmatched parts. ... In this paper we present an algorithm for detecting and repairing defects in

*the*boundary of a

*polyhedron*. ... Acknowledgment

*The*authors wish to thank Haim Wolfson for useful discussions concerning

*the*geometric hashing technique and its applications. ...

##
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Reconstruction of Branching Surface and Its Smoothness by Reversible Catmull-Clark Subdivision
[chapter]

2009
*
Lecture Notes in Computer Science
*

In branching, a particular layer has more than

doi:10.1007/978-3-642-01973-9_85
fatcat:jke7aywmhfdj7edxauuiw2pgye
*one*contour, corresponds with*the*contour at*the**adjacent*layer. ... In*the*next step, 3D composite curves are converted into different*polyhedrons*by*the*help of*the*contours at*adjacent*layers. ... (a) (*b*) (c)*Polyhedrons*are constructed for all*the*pairs of*adjacent*layers once there is no branching problem. ...##
###
Combinatorial structure and adjacency of vertices of polytope of b-factors

2014
*
Russian Mathematics (Izvestiya VUZ. Matematika)
*

In

doi:10.3103/s1066369x14060061
fatcat:go5yjfygi5ajljkp3gvrnowod4
*the*present paper in terms of*the*graph theory we describe*the*structure and*vertices**adjacency*criterion of*b*-factors*polyhedron*.*The*special attention is paid to nonintegral*vertices*. ... Results of*the*present paper, in particular, generalize properties of nonintegral*vertices*of TSP*polyhedron*, give*vertices**adjacency*criterion of a transportation polytope. ... Thus we obtain*one*-to-*one*correspondence between 2 E and*the*set of*vertices*of*the*unit cube in R E . ...##
###
Graph-theoretical conditions for inscribability and Delaunay realizability

1996
*
Discrete Mathematics
*

A

doi:10.1016/0012-365x(95)00276-3
fatcat:rcsqpuezeffhloyk5tsufujesa
*polyhedron*is of inscribable type if it has a combinatorially equivalent realization as*the*convex hull of a set of points*on*a sphere. ... Specifically, we show that any nonbipartite*polyhedron*of inscribable type has a perfect*matching*containing any specified edge, and that any bipartite*polyhedron*of inscribable type has a perfect*matching*... There is no perfect*matching*in which a is*matched*with*b*and c is*matched*with a vertex outside triangle abc. Proof. Suppose that G is bipartite and of inscribable type with 2n*vertices*. ...##
###
Topological recognition of polyhedral objects from multiple views

2001
*
Artificial Intelligence
*

*The*topological nature of

*the*AG also suggests a topological

*match*of images of

*the*unknown object and stored aspects. ... First, we discuss

*the*topological

*matching*process, and give a suitable topological definition of aspect. ... A simpler approach consists in finding only if

*one*topological

*match*exist, without attempting to

*match*

*the*corresponding

*vertices*of two

*adjacent*aspects in

*the*AG with

*the*corresponding

*vertices*of two ...

##
###
Regular non-hamiltonian polyhedral graphs

2018
*
Applied Mathematics and Computation
*

*The*duals of

*the*planar graphs G ∩ A and G ∩

*B*are trees, so we may colour their

*vertices*alternatingly. ... We have that Furthermore, for each even n ≥ 38 there is a non-hamiltonian cubic

*polyhedron*

*on*n

*vertices*. Balinski asked whether non-traceable cubic polyhedra exist. ...

*The*computational resources (Stevin Supercomputer Infrastructure) and services used in this work were provided by

*the*VSC (Flemish Supercomputer Center), funded by Ghent University, FWO and

*the*Flemish ...

##
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On correlation of hyperbolic volumes of fullerenes with their properties
[article]

2020
*
arXiv
*
pre-print

*One*of

*the*most important invariants of such a

*polyhedron*is its volume. We are referring this volume as a hyperbolic volume of a fullerene. ...

*The*correlation between hyperbolic volume of fullerene and its Wiener index suggested few conjectures

*on*volumes of hyperbolic polyhedra. ... Since each fullerene can be realized as a bounded right-angled hyperbolic

*polyhedron*, we can

*match*each fullerene with

*the*hyperbolic volume of

*the*corresponding hyperbolic

*polyhedron*. ...

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