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On the covering graph of balanced lattices

1996
*
Discrete Mathematics
*

Modifying some

doi:10.1016/0012-365x(95)00061-z
fatcat:e5ic2aq55vd25goid75zscicz4
*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 ...##
###
Voltage-Graphic Matroids
[chapter]

2010
*
Matroid Theory and its Applications
*

Let χ b X (λ) denote

doi:10.1007/978-3-642-11110-5_8
fatcat:re4hnhhc4fhlvhbiadsjmmfqtq
*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. ...##
###
On centrally symmetric graphs

1996
*
Mathematica Bohemica
*

I am grateful to

doi:10.21136/mb.1996.125944
fatcat:ttbb7m624ncnzk2mqv7jhitqui
*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. ...##
###
Periodic networks of fixed degree minimizing length
[article]

2019
*
arXiv
*
pre-print

We study networks in ^n which are periodic under a

arXiv:1911.01792v1
fatcat:kmepcgn7qrcd7guikv5b7277mu
*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. ...##
###
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]

2020
*
arXiv
*
pre-print

Applications

arXiv:1908.05797v2
fatcat:u5kgqwyt5zcm3nyxdea2r2rvdq
*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. ...##
###
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

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. ...

##
###
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]

2020
*
arXiv
*
pre-print

We give

arXiv:2003.08917v2
fatcat:acp4l4ka6vdzdmosgxbhbz4thi
*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. ...##
###
Bipartite Perfect Matching as a Real Polynomial
[article]

2020
*
arXiv
*
pre-print

Our proof relies heavily

arXiv:2001.07642v2
fatcat:qznfje7axzberp3yo2k36qhhvm
*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 ...##
###
Entanglement in doped resonating valence bond states

2008
*
Physical Review B
*

We investigate

doi:10.1103/physrevb.78.224513
fatcat:7oztkpypbbdl3gtq6t72at7sju
*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 ...##
###
Author index

2002
*
Discrete Mathematics
*

Salvi,

doi:10.1016/s0012-365x(02)00738-0
fatcat:nspeq6c56za2hjedmozlhkc3r4
*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. ...##
###
Signed lozenge tilings
[article]

2015
*
arXiv
*
pre-print

It is well-known that plane partitions, lozenge tilings

arXiv:1507.02507v1
fatcat:yxmocka65jasxlmgo3oroos3nq
*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. ...##
###
Forthcoming papers

1991
*
Discrete Mathematics
*

Jerxy Topp and Lutz Volkmann,

doi:10.1016/0012-365x(91)90170-7
fatcat:6hztupe3s5bwbihfiju4l5giuy
*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)). ...
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