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Z-transformation graphs of perfect matchings of plane bipartite graphs

2004
*
Discrete Mathematics
*

Let G be a

doi:10.1016/s0012-365x(03)00319-4
fatcat:tcabyoigvnayjpsv33osi7w4ky
*plane**bipartite**graph*with at least two*perfect**matchings*. ... The*Z*-*transformation**graph*, ZF (G),*of*G with respect to a speciÿc set F*of*faces is deÿned as a*graph*on the*perfect**matchings**of*G such that two*perfect**matchings*M1 and M2 are adjacent provided M1 and ... Here we would like to mention that it was proved that the*block**graph**of*the*Z*-*transformation**graph**Z**of*a*plane**elementary**bipartite**graph*is a path by orientating all the edges*of**Z*in a certain way ...##
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Z -transformation graphs of maximum matchings of plane bipartite graphs

2004
*
Discrete Applied Mathematics
*

Let G be a

doi:10.1016/s0166-218x(03)00305-6
fatcat:px437d5p2rhvbftq42gz6244ke
*plane**bipartite**graph*. The*Z*-*transformation**graph**Z*(G) and its orientationZ(G) on the maximum*matchings**of*G are deÿned. ... This paper mainly shows that some basic results for*Z*-*transformation**graph*(digraph)*of*a*plane**elementary**bipartite**graph*still hold for every nontrivial component*of**Z*(G) (*Z*(G)). ... Let G be a*plane**elementary**bipartite**graph*. Then the*block**graph**of**Z*-*transformation**graph**of*G is a path (cf. Fig. 3 ). ...##
###
Page 6746 of Mathematical Reviews Vol. , Issue 2004i
[page]

2004
*
Mathematical Reviews
*

(PRC-LAN; Lanzhou

*Z*-*transformation**graphs**of*maximum*matchings**of**plane**bipartite**graphs*. ... A directed version*of*the*Z*-*transformation**graph**of*a*plane**bipartite**graph*is also studied. Charles H. C. ...##
###
Plane elementary bipartite graphs

2000
*
Discrete Applied Mathematics
*

Second, the concept

doi:10.1016/s0166-218x(00)00204-3
fatcat:m7zs3kflxzct3bu3zpme6xf5m4
*of*the*Z*-*transformation**graph**Z*(G)*of*a hexagonal system G (whose vertices represent the*perfect**matchings**of*G) is extended to a*plane**bipartite**graph*G and some results analogous ...*of*G) and whose*Z*-*transformation**graphs**Z*(G) contain vertices*of*degree one. ? ... A*plane**elementary**bipartite**graph*G with a*perfect**matching*M ; (b). The*Z*-*transformation**graph**Z*(G) with two cut vertices M and M ⊕ C. ...##
###
Page 4633 of Mathematical Reviews Vol. , Issue 2000g
[page]

2000
*
Mathematical Reviews
*

”] (PRC-LAN; Lanzhou);
Zhang, Fuji (PRC-XIAM; Xiamen)

*Block**graphs**of**Z*-*transformation**graphs**of**perfect**matchings**of**plane**elementary**bipartite**graphs*. ... For a*plane**elementary**bipartite**graph*G it is shown that the*block**graph**of**Z*-*transformation**graph**Z*(G) is a path. ...##
###
The connectivity of Z-transformation graphs of perfect matchings of polyominoes

1996
*
Discrete Mathematics
*

The

doi:10.1016/0012-365x(95)00048-2
fatcat:m6t4y64b55fw5arjyf4j5gxnrm
*Z*-*transformation**graph**Z*(G)*of*a polyomino G is a*graph*in which the vertices are the*perfect**matchings**of*G and two vertices are adjacent provided that the union*of*the corresponding two*perfect**matchings*... This paper presents some properties*of*polyominoes with*perfect**matchings*and mainly shows that the connectivity*of**Z*(G) reaches its minimum degree with only two exceptions. ... This work is supported by the National Natural Foundation*of*China and Youth Foundation*of*Lanzhou University. 272 H. ...##
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Page 59 of Mathematical Reviews Vol. , Issue 2000a
[page]

2000
*
Mathematical Reviews
*

The

*Z*-*transformation**graph**Z*(H) is the*graph*where the vertices are the*perfect**match*- ings*of*H and where two*perfect**matchings*are joined by an edge provided their symmetric difference is a hexagon*of*... Michal Penn (IL-TECHMG; Haifa) 2000a:05164 05C70 05C90 Zhang, Lian Zhu (PRC-ZZTC; Zhangzhou) The*Z*-*transformation**graph**of**perfect**matchings**of*a catacondensed hexagonal system. (Chinese. ...##
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Extremal anti-forcing numbers of perfect matchings of graphs
[article]

2016
*
arXiv
*
pre-print

The anti-forcing number

arXiv:1607.05392v1
fatcat:whntkeqq5jbhthreav36zxneku
*of*a*perfect**matching*M*of*a*graph*G is the minimal number*of*edges not in M whose removal to make M as a unique*perfect**matching**of*the resulting*graph*. ... In this paper, we characterize the*plane**elementary**bipartite**graph*whose minimum anti-forcing number is one. We show that the maximum anti-forcing number*of*a*graph*is at most its cyclomatic number. ... Anti-forcing edge The*Z*-*transformation**graph**Z*(G)*of*a*plane**bipartite**graph*G is defined as the*graph*whose vertices represent the*perfect**matchings**of*G where two vertices are adjacent if and only if ...##
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Characterization of reducible hexagons and fast decomposition of elementary benzenoid graphs

2008
*
Discrete Applied Mathematics
*

A hexagon h

doi:10.1016/j.dam.2007.08.029
fatcat:57leuv3bxreazda24jiduouwe4
*of*an*elementary*benzenoid*graph*is reducible, if the removal*of*boundary edges and vertices*of*h results in an*elementary*benzenoid*graph*. ... A benzenoid*graph*is a finite connected*plane**graph*with no cut vertices in which every interior region is bounded by a regular hexagon*of*a side length one. ... concept*of*the resonance*graphs*(also called the*Z*-*transformation**graphs*) [1, 8, 10, 16, 19] . ...##
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Resonance Graphs and a Binary Coding for the 1-Factors of Benzenoid Systems

2008
*
SIAM Journal on Discrete Mathematics
*

Applying the recently obtained distributive lattice structure on the set

doi:10.1137/070699287
fatcat:4cybmafjnrboxnu4lsf3fyud7e
*of*1-factors, we show that the resonance*graphs**of*any benzenoid systems G, as well as*of*general*plane*(weakly)*elementary**bipartite*... The labelling preserves the partial ordering*of*the above-mentioned lattice and can be*transformed*into a binary coding for the 1-factors. ... The authors are grateful to the referee for giving valuable suggestions to the improvement*of*this manuscript. ...##
###
Kasteleyn cokernels
[article]

2002
*
arXiv
*
pre-print

We consider Kasteleyn and Kasteleyn-Percus matrices, which arise in enumerating

arXiv:math/0108150v2
fatcat:yemc7bjly5emrdfepn7uc4p274
*matchings**of*planar*graphs*, up to matrix operations on their rows and columns. ... We apply these ideas to*plane*partitions and related planar*of*tilings. ... If M is a Kasteleyn-Percus matrix for an unweighted*bipartite*, planar*graph*G with at least one*perfect**matching*, then two such sets to consider are coker M and P, the set*of**perfect**matchings**of*G. ...##
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Parameterizing the Permanent: Hardness for K_8-minor-free graphs
[article]

2021
*
arXiv
*
pre-print

This stirred up hopes that counting

arXiv:2108.12879v1
fatcat:5xxn3mm42janjfcbc4kocfiswe
*perfect**matchings*might be polynomial-time solvable for*graph*classes excluding any fixed minor H. ... In the 1960s, statistical physicists discovered a fascinating algorithm for counting*perfect**matchings*in planar*graphs*. Valiant later showed that the same problem is #P-hard for general*graphs*. ... Evaluating permanents is equivalent to counting*perfect**matchings*in*bipartite**graphs*: Given a*bipartite*input*graph*G on n + n vertices with its n × n bi-adjacency matrix A, the permanent per(A) counts ...##
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Bipartite Field Theories, Cluster Algebras and the Grassmannian
[article]

2014
*
arXiv
*
pre-print

and the Grassmannian, and applications to

arXiv:1404.3752v1
fatcat:luxnvtcffnck7aq7vdejqtsfim
*graph*equivalence and stratification*of*the Grassmannian. ... We review recent progress in*Bipartite*Field Theories. ... and the Grassmannian, and applications to*graph*equivalence and stratification*of*the Grassmannian. ...##
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Master index of volumes 171–180

1998
*
Discrete Mathematics
*

Zheng,

doi:10.1016/s0012-365x(97)86438-2
fatcat:5pjlekl7wzgjtbdluqgggziz7q
*Perfect**matchings*and ears in*elementary**bipartite**graphs*Harary, F., see M. Gionfriddo Hatcher, R.L., see J. Berenbom Hattingh, J.H. and E. ... Fiol, Connectivity*of*large*bipartite*digraphs and*graphs*174 (1997) 3-17 Balbuena, M.C., A. Carmona, J. Fabrega and M.A. ...##
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Kasteleyn theorem, geometric signatures and KP-II divisors on planar bipartite networks in the disk
[article]

2021
*
arXiv
*
pre-print

Maximal minors

arXiv:2012.13797v3
fatcat:sl6cug4qtvcwbdjfv3y27j7n5i
*of*Kasteleyn sign matrices on planar*bipartite**graphs*in the disk count dimer configurations with prescribed boundary conditions, and the weighted version*of*such matrices provides a natural ... Indeed the KP wave function solves such system*of*relations at the nodes*of*the spectral curve if the dual*graph**of*the latter represents the soliton data. ... I also thank the referee*of*the paper for valuable remarks. ...
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