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On the covering graph of balanced lattices

Manfred Stern
1996 Discrete Mathematics  
Modifying some of the results of Duffus and Rival we give a common generalization proved for lattices which are balanced and graded. 0012-365X/96/$15.00 (~ 1996 Elsevier Science B.V.  ...  Jakubik has shown that for discrete modular lattices all graph isomorphisms are given by certain direct product decompositions.  ...  Acknowledgements This paper was rewritten during a stay at the Laboratoire de Mathtmatiques Discr&es in Marseille-Luminy in February/March 1994 which is ~atefully acknowledged to the CNRS of France and  ... 
doi:10.1016/0012-365x(95)00061-z fatcat:e5ic2aq55vd25goid75zscicz4

Voltage-Graphic Matroids [chapter]

Thomas Zaslavsky
2010 Matroid Theory and its Applications  
Let χ b X (λ) denote the balanced chromatic polynomial of the induced voltage graph on X ⊆ N . Then Chromatic Polynomial Theorem. χ Φ (µg + 1) is a polynomial in µ.  ...  The lattice of flats is the set of spanning forests of Γ. 6) ED( Γ), the equidirected circle matroid of a digraph Γ (Matthews): G = Z, ϕ(e) = +1 when e is taken in the direction assigned by Γ.  ...  The lattice of all intersections of subsets of H[Φ], ordered by reverse inclusion, is isomorphic to the lattice of flats of G(Φ). Corollary. H[ 4.  ... 
doi:10.1007/978-3-642-11110-5_8 fatcat:re4hnhhc4fhlvhbiadsjmmfqtq

On centrally symmetric graphs

Manfred Stern
1996 Mathematica Bohemica  
I am grateful to the CNRS of France for inviting me to the Laboratoire de Mathematiques Discretes in Marseille, Luminy, during February/March 1994. In particular I thank Professor G.  ...  If the covering graph of a lattice is a CS-graph or an S-graph, then the lattice will be called a CS-lattice or S-lattice, respectively.  ...  Kotzig [7] conjectured that a graph is centrally symmetric if and only if it is the covering graph of the direct product of lattices, each isomorphic to K2n for some integer n. E.  ... 
doi:10.21136/mb.1996.125944 fatcat:ttbb7m624ncnzk2mqv7jhitqui

Periodic networks of fixed degree minimizing length [article]

Jerome Alex, Karsten Grosse-Brauckmann
2019 arXiv   pre-print
We study networks in ^n which are periodic under a lattice of rank n and have vertices of prescribed degree d> 3.  ...  We minimize the length of the quotient networks, subject to the constraint that the fundamental domain has n-dimensional volume 1.  ...  For all other d ≥ n + 1, the network N covers one of the graphs D ,k where 2 ≤ k ≤ d and d − k = 2 . Proof.  ... 
arXiv:1911.01792v1 fatcat:kmepcgn7qrcd7guikv5b7277mu

Page 1837 of Mathematical Reviews Vol. , Issue 86e [page]

1986 Mathematical Reviews  
The notion of a perfect zero-one matrix is closely related to that of a perfect graph as well as that of a balanced matrix as introduced by C. Berge [ibid. 2 (1972), no. 1, 19-31; MR 48 #142].  ...  belong to and cover the set T.  ... 

Invariant synchrony subspaces of sets of matrices [article]

John M. Neuberger, Nandor Sieben, James W. Swift
2020 arXiv   pre-print
Applications of these invariant synchrony subspaces include equitable and almost equitable partitions of the vertices of a graph used in many areas of graph theory, balanced and exo-balanced partitions  ...  We also present what we call the split and cir algorithm for finding the lattice of invariant synchrony subspaces. Our theory and algorithm is further generalized for non-square matrices.  ...  (ii) Steps in the split and cir algorithm for finding the lattice of balanced partitions. Straight arrows point to lower covers, corresponding to splits.  ... 
arXiv:1908.05797v2 fatcat:u5kgqwyt5zcm3nyxdea2r2rvdq

Page 1873 of Mathematical Reviews Vol. , Issue 94d [page]

1994 Mathematical Reviews  
The ordered version of this problem is: Which finite posets P occur as cover-preserving subposets of a Boolean lattice?  ...  The antichain covering number is considered also in connection with comparability graphs and infinite ordered sets, namely: if a(P) is countable, then the comparability graph of P is perfect if and only  ... 

Signed graphs

Thomas Zaslavsky
1982 Discrete Applied Mathematics  
The concepts of balance, switching, restriction and contraction, double covering graphs, and linear representation of signed graphs are treated in terms of the matroid, and a matrix-tree theorem for signed  ...  This article introduces the matroids of signed graphs, which generalize both the polygon matroids and the even-circle (or unoriented cycle) matroids of ordinary graphs.  ...  And I thank Jeff Lagarias for his advice on the manuscript.  ... 
doi:10.1016/0166-218x(82)90033-6 fatcat:6bs725v34vfmnnzrvmdiqe5lqm

Page 6177 of Mathematical Reviews Vol. , Issue 90K [page]

1990 Mathematical Reviews  
This survey covers the theory of distributive lattices, Boolean lattices and lattices close to them.  ...  Balanced graphs, that is, graphs with no half-edges and all circles balanced, are studied.  ... 

A Real Polynomial for Bipartite Graph Minimum Weight Perfect Matchings [article]

Thorben Tröbst, Vijay V. Vazirani
2020 arXiv   pre-print
We give the real multilinear polynomial for the Boolean function which determines if a graph G ⊆ K_n,n contains one of these minimum weight perfect matchings.  ...  We give the following generalization: Given an arbitrary non-negative weight function w on the edges of K_n,n, consider its set of minimum weight perfect matchings.  ...  K n,n denotes the complete balanced bipartite graph on 2n vertices.  ... 
arXiv:2003.08917v2 fatcat:acp4l4ka6vdzdmosgxbhbz4thi

Bipartite Perfect Matching as a Real Polynomial [article]

Gal Beniamini, Noam Nisan
2020 arXiv   pre-print
Our proof relies heavily on the fact that the lattice of graphs which are "matching-covered" is Eulerian.  ...  In contrast, we show that in the dual representation (switching the roles of 0 and 1) the number of monomials is only exponential in Θ(n log n).  ...  Using The Eulerian Matching-Covered Lattice The characterization of BP M ⋆ n as a graph cover function for the lattice of graphs covered by Hall violators allowed us to restrict the set of monomials that  ... 
arXiv:2001.07642v2 fatcat:qznfje7axzberp3yo2k36qhhvm

Entanglement in doped resonating valence bond states

Ravishankar Ramanathan, Dagomir Kaszlikowski, Marcin Wiesniak, Vlatko Vedral
2008 Physical Review B  
We investigate the entanglement properties of resonating valence bond states on a two dimensional lattice in the presence of dopants that remove electrons from the lattice creating "holes".  ...  We argue that there is a particular density of dopants (holes) where the entanglement contained in the lattice attains its maximal value for the nearest-neighbour RVB liquid state.  ...  It is apparent that each dimer covering of the RVB structure can be represented as a balanced bipartite graph with the sublattices A and B forming the two vertex sets, there being L edges in a 2L site  ... 
doi:10.1103/physrevb.78.224513 fatcat:7oztkpypbbdl3gtq6t72at7sju

Author index

2002 Discrete Mathematics  
Salvi, On the rank polynomial of the lattice of order ideals of fences and crowns (1-3) 163-177 Nishimura, T., A closure concept in factor-critical graphs (Note) (1-3) 319-324  ...  Le, A criterion for the applicability of Zeilberger', S.D. and Y.-G. Chen, On a question regarding visibility of lattice points-III (Note) (1-3) 251-256 Atkinson, M.D. and T.  ... 
doi:10.1016/s0012-365x(02)00738-0 fatcat:nspeq6c56za2hjedmozlhkc3r4

Signed lozenge tilings [article]

David Cook II, Uwe Nagel
2015 arXiv   pre-print
It is well-known that plane partitions, lozenge tilings of a hexagon, perfect matchings on a honeycomb graph, and families of non-intersecting lattice paths in a hexagon are all in bijection.  ...  As a consequence, we obtain the equality of determinants, up to sign, that enumerate signed perfect matchings and signed families of lattice paths of a triangular region, respectively.  ...  It is the zero-one matrix Z(T ) of (i) The graph G(T ). (ii) Selected covered edges. (iii) The perfect matching.  ... 
arXiv:1507.02507v1 fatcat:yxmocka65jasxlmgo3oroos3nq

Forthcoming papers

1991 Discrete Mathematics  
Jerxy Topp and Lutz Volkmann, On packing and covering numbers of graphs In this paper we present a characterization of connected graphs of order (k + 1)n with k-covering number n, a characterization of  ...  Forthcoming papers John Sheehan, Balanced graphs with minimum degree constraints Let G be a finite simple graph on n vertices with minimum degree 6 = 6(G) (n = 6 (mod 2)).  ... 
doi:10.1016/0012-365x(91)90170-7 fatcat:6hztupe3s5bwbihfiju4l5giuy
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