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Adjacent vertices on the b-matching polyhedron

Dirk Hausman
1981 Discrete Mathematics  
Therelfore we ch:iracterize here 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  ... 
doi:10.1016/0012-365x(81)90256-9 fatcat:rfdvb7hdfvcc3fazqbiz7mjcie

Adjacency on combinatorial polyhedra

Tomomi Matsuia, Sunao Tamura
1995 Discrete Applied Mathematics  
We consider a path 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.  ... 
doi:10.1016/0166-218x(94)00092-r fatcat:odmniuhyezbzhghqp2ullqlftm

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  ... 

Hamiltonicity and combinatorial polyhedra

D Naddef, W.R Pulleyblank
1981 Journal of combinatorial theory. Series B (Print)  
We say that a 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  ... 
doi:10.1016/0095-8956(81)90032-0 fatcat:sc5ozzhe7jay7ofeagiifhasde

Hamiltonicity in (0–1)-polyhedra

D.J Naddef, W.R Pulleyblank
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.  ... 
doi:10.1016/0095-8956(84)90043-1 fatcat:q4zuoq5sezg75msgqgcyi2z7ue

The zipper foldings of the diamond

Erin W. Chambers, Di Fang, Kyle A. Sykes, Cynthia M. Traub, Philip Trettenero
2015 Involve. A Journal of Mathematics  
In our foldings, all polyhedra will have at most 6 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.  ... 
doi:10.2140/involve.2015.8.521 fatcat:zwv242hca5a57n26yif2rm3oge

Characterizations of adjacency on the branching polyhedron

Rick Giles, Dirk Hausmann
1979 Discrete Mathematics  
Given two distinct branchings of a directed graph G, we present several conditions which are equivalent to 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.  ... 
doi:10.1016/0012-365x(79)90027-x fatcat:tdshoebjejdihnq3lyijxdooqm

Pancyclic properties of the graph of some 0–1 polyhedra

Denis Naddef
1984 Journal of combinatorial theory. Series B (Print)  
In this paper it is shown that a certain class of (&l) polyhedra, which includes 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.  ... 
doi:10.1016/0095-8956(84)90040-6 fatcat:p5zqiqu7efei7i4y6fiwjf2v44

Filling gaps in the boundary of a polyhedron

Gill Barequet, Micha Sharir
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.  ... 
doi:10.1016/0167-8396(94)00011-g fatcat:gpqh637e2nha3miadibkz2j2wu

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

Kailash Jha
2009 Lecture Notes in Computer Science  
In branching, a particular layer has more than 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.  ... 
doi:10.1007/978-3-642-01973-9_85 fatcat:jke7aywmhfdj7edxauuiw2pgye

Combinatorial structure and adjacency of vertices of polytope of b-factors

R. Yu. Simanchev
2014 Russian Mathematics (Izvestiya VUZ. Matematika)  
In 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 .  ... 
doi:10.3103/s1066369x14060061 fatcat:go5yjfygi5ajljkp3gvrnowod4

Graph-theoretical conditions for inscribability and Delaunay realizability

Michael B. Dillencourt, Warren D. Smith
1996 Discrete Mathematics  
A 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.  ... 
doi:10.1016/0012-365x(95)00276-3 fatcat:rcsqpuezeffhloyk5tsufujesa

Topological recognition of polyhedral objects from multiple views

Aldo Laurentini
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  ... 
doi:10.1016/s0004-3702(01)00055-8 fatcat:zskgqrgrqbewlit65zj7sossf4

Regular non-hamiltonian polyhedral graphs

Nico Van Cleemput, Carol T. Zamfirescu
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  ... 
doi:10.1016/j.amc.2018.05.062 fatcat:hecq3pdksrb2xat7ssxjlh3v3a

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

Andrey Egorov, Andrei Vesnin
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.  ... 
arXiv:2011.02711v1 fatcat:mhcwmtii2vghfncgyeosgnoedi
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