Filters








627 Hits in 5.8 sec

Z-transformation graphs of perfect matchings of plane bipartite graphs

Heping Zhang, Fuji Zhang, Haiyuan Yao
2004 Discrete Mathematics  
Let G be a 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  ... 
doi:10.1016/s0012-365x(03)00319-4 fatcat:tcabyoigvnayjpsv33osi7w4ky

Z -transformation graphs of maximum matchings of plane bipartite graphs

Heping Zhang, Rijun Zha, Haiyuan Yao
2004 Discrete Applied Mathematics  
Let G be a 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 ).  ... 
doi:10.1016/s0166-218x(03)00305-6 fatcat:px437d5p2rhvbftq42gz6244ke

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

Heping Zhang, Fuji Zhang
2000 Discrete Applied Mathematics  
Second, the concept 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.  ... 
doi:10.1016/s0166-218x(00)00204-3 fatcat:m7zs3kflxzct3bu3zpme6xf5m4

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

Heping Zhang
1996 Discrete Mathematics  
The 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.  ... 
doi:10.1016/0012-365x(95)00048-2 fatcat:m6t4y64b55fw5arjyf4j5gxnrm

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.  ... 

Extremal anti-forcing numbers of perfect matchings of graphs [article]

Kai Deng, Heping Zhang
2016 arXiv   pre-print
The anti-forcing number 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  ... 
arXiv:1607.05392v1 fatcat:whntkeqq5jbhthreav36zxneku

Characterization of reducible hexagons and fast decomposition of elementary benzenoid graphs

Andrej Taranenko, Aleksander Vesel
2008 Discrete Applied Mathematics  
A hexagon h 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] .  ... 
doi:10.1016/j.dam.2007.08.029 fatcat:57leuv3bxreazda24jiduouwe4

Resonance Graphs and a Binary Coding for the 1-Factors of Benzenoid Systems

Heping Zhang, Peter Che Bor Lam, Wai Chee Shiu
2008 SIAM Journal on Discrete Mathematics  
Applying the recently obtained distributive lattice structure on the set 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.  ... 
doi:10.1137/070699287 fatcat:4cybmafjnrboxnu4lsf3fyud7e

Kasteleyn cokernels [article]

Greg Kuperberg
2002 arXiv   pre-print
We consider Kasteleyn and Kasteleyn-Percus matrices, which arise in enumerating 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.  ... 
arXiv:math/0108150v2 fatcat:yemc7bjly5emrdfepn7uc4p274

Parameterizing the Permanent: Hardness for K_8-minor-free graphs [article]

Radu Curticapean, Mingji Xia
2021 arXiv   pre-print
This stirred up hopes that counting 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  ... 
arXiv:2108.12879v1 fatcat:5xxn3mm42janjfcbc4kocfiswe

Bipartite Field Theories, Cluster Algebras and the Grassmannian [article]

Sebastian Franco, Daniele Galloni, Alberto Mariotti
2014 arXiv   pre-print
and the Grassmannian, and applications to 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.  ... 
arXiv:1404.3752v1 fatcat:luxnvtcffnck7aq7vdejqtsfim

Master index of volumes 171–180

1998 Discrete Mathematics  
Zheng, 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.  ... 
doi:10.1016/s0012-365x(97)86438-2 fatcat:5pjlekl7wzgjtbdluqgggziz7q

Kasteleyn theorem, geometric signatures and KP-II divisors on planar bipartite networks in the disk [article]

Simonetta Abenda
2021 arXiv   pre-print
Maximal minors 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.  ... 
arXiv:2012.13797v3 fatcat:sl6cug4qtvcwbdjfv3y27j7n5i
« Previous Showing results 1 — 15 out of 627 results