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Orientable quadrilateral embeddings of products of graphs

1992
*
Discrete Mathematics
*

., Orientable 109 (1992) 203-205.

doi:10.1016/0012-365x(92)90291-m
fatcat:5oexlxqlc5hw7jajz4tlm2yxri
*quadrilateral**embeddings**of*products*of**graphs*, Discrete Mathematics It is proved that for each connected regular*graph*G there exists an integer m > 0 such that for each ... integer n am the Cartesian product G x Q, has an orientable*quadrilateral**embedding*, thereby extending the result from*bipartite*to regular nonbipartite*graphs*. ... White for careful reading*of*the manuscript and for helpful hints and suggestions. As a matter*of*fact recent joint work in progress with A.T. ...##
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Nonorientable genus of nearly complete bipartite graphs

1988
*
Discrete & Computational Geometry
*

In particular, it is shown that G(5,4,4) and G(5, 5, 5) have no nonorientable

doi:10.1007/bf02187903
fatcat:otdkgt36gve3hk5axnq24fz4iq
*quadrilateral**embedding*. ... Let G(m, n, k), m, n > 3, k-< min(m, n), be the*graph*obtained from the complete*bipartite**graph*K,.. by deleting an arbitrary set*of*k independent edges, and let It is shown that the nonorientable genus ... On the other hand, genus*embeddings**of*some more "general"*bipartite**graphs*with many edges can also be obtained using similar methods as in this paper. ...##
###
Page 3797 of Mathematical Reviews Vol. , Issue 85i
[page]

1985
*
Mathematical Reviews
*

The techniques in this paper are used to show that in addition,

*quadrilateral**embedding**of*a*bipartite**graph*G with at least 3 vertices can be lifted to a*quadrilateral**embedding**of*G[K,,| for every odd ... D. (1-PAS)*Embeddings**of**bipartite**graphs*. J.*Graph*Theory 7 (1983), no. 3, 325-334. ...##
###
Nonorientable Embeddings of Groups

1988
*
European journal of combinatorics (Print)
*

*Embeddings*

*of*Cayley

*graphs*into nonorientable surfaces are studied. Some lower and upper bounds for the nonorientable genus

*of*abelian and hamiltonian groups are obtained. ... In some cases the method is applied to orientable

*embeddings*. ... ACKNOWLEDGEMENTS The authors acknowledge the help

*of*Chris Godsil with the proof

*of*Proposition 5. ...

##
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Graph-Theoretic Solutions to Computational Geometry Problems
[chapter]

2010
*
Lecture Notes in Computer Science
*

,
all interior faces

doi:10.1007/978-3-642-11409-0_1
fatcat:rqrljmkgqrb3ddw5nszva6ighi
*quadrilaterals*, all interior vertex degrees ≥ 4 (*bipartite*, median*graph*) Kinggraph: add diagonals*of*quads Guaranteed to be 4-chromatic 4-color, use smallest color class ... having pq as their diameter = max ind. set*of**bipartite**graph*Dynamic*graph*algorithm for multiple*bipartite*MIS's [E. & Erickson 1994] To find max cluster size for given diameter D: For each input ...*Embedding*: 1-1 function from the points*of*one metric space to another dilation*of*a single distance: distortion*of**embedding*= worst ratio*of*dilations if*embedding*scaled so all distances nondecreasing ...##
###
Dimers and Circle patterns
[article]

2020
*
arXiv
*
pre-print

We establish a correspondence between the dimer model on a

arXiv:1810.05616v2
fatcat:3hnnbhodgjbdxoscnbfow3kwqq
*bipartite**graph*and a circle pattern with the combinatorics*of*that*graph*, which holds for*graphs*that are either planar or*embedded*on the torus ... The set*of*positive face weights on the*graph*gives a set*of*global coordinates on the space*of*circle patterns with*embedded*dual. ... Acknowledgements We are grateful to Dmitry Chelkak for sharing his ideas during many fruitful exchanges, and providing the proof*of*Lemma 11. R. Kenyon ...##
###
Page 2114 of Mathematical Reviews Vol. , Issue 97D
[page]

1997
*
Mathematical Reviews
*

Summary: “Let G be a

*bipartite**graph*with a*quadrilateral*(or self-dual)*embedding*. ... (SAR-UPAM; Dhahran) Self-dual*embeddings**of*the composition*of**bipartite**graphs*. (English summary)*Graph*theory, combinatorics, and algorithms, Vol. \, 2 (Kalamazoo, MI, 1992), 1-4, Wiley-Intersci. ...##
###
The construction and classification of self-dual spherical polyhedra

1992
*
Journal of combinatorial theory. Series B (Print)
*

In this paper we consider spherical polyhedra, or equivalently 3-connected

doi:10.1016/0095-8956(92)90065-6
fatcat:vzhcz3ljvvcfljahzpt7toja7u
*embedded*planar*graphs*. A self-duality map sends vertices to faces and faces to vertices while preserving incidence. ... Included is the construction*of*polyhedra which admit only self-duality maps*of*large order. (i3 ... It follows that R -E(A,) is an*embedded**bipartite**graph*with each face a*quadrilateral*or a hexagon. ...##
###
On the genus of the tensor product of graphs where one factor is a regular graph

1994
*
Discrete Mathematics
*

Assuming that H is suitably imbedded in some orientable surface by modifying the edges

doi:10.1016/0012-365x(93)e0057-b
fatcat:7ehxteqeanayxex6q5jinfa3am
*of*H according to the configuration*of*G we get the permutation voltage*graph*H c2') whose permutation derived*graph*... The tensor product HOG where G is a 2k-regular*graph*can be regarded as a covering space*of*the permutation voltage*graph*H czk) obtained from H. ... where H is a*bipartite*(p, q)*graph*which has an orientable*quadrilateral*imbedding. ...##
###
The largest demigenus of a bipartite signed graph

2001
*
Discrete Mathematics
*

We ÿnd the smallest surface within which it is possible to orientation-embed the complete

doi:10.1016/s0012-365x(00)00349-6
fatcat:rlrg7wqfhvafhgmrvvbbmjntaq
*bipartite*signed*graph*±Kr;s, which is obtained from the complete*bipartite**graph*Kr;s through replacing each edge ... A*graph*with signed edges is orientation*embedded*in a surface when it is topologically*embedded*so that one trip around a closed path preserves or reverses orientation according as the path's sign product ...*Quadrilaterality*. Since a minimal*embedding**of*K 2r; 2s has only*quadrilateral*faces, the same holds true for a minimal*embedding**of*±K r; s . ...##
###
Page 5880 of Mathematical Reviews Vol. , Issue 93k
[page]

1993
*
Mathematical Reviews
*

Giorgio Balconi (I-PAVI-G)
COMBINATORICS
93k:05053 05C10 Pisanski, Tomaz (SV-LJUB) Orientable

*quadrilateral**embeddings**of*products*of**graphs*. ... The main result*of*this paper is that a connected projective-planar*graph*G which is not planar has a projective-planar*embedding*with only even faces if and only if either G is*bipartite*or B(G) is planar ...##
###
Tight embeddings of partial quadrilateral packings

2010
*
Journal of combinatorial theory. Series A
*

Include the

doi:10.1016/j.jcta.2009.06.003
fatcat:wt7fbz6nljhnrj7eziuhtnciqa
*quadrilaterals*(a 1 , a 2 , a 3 , b 1 ), (a 3 , a 4 , a 5 , b 2 ), (b 1 , a 2 , b 2 , a 4 ), and add a C 4 -decomposition*of*the complete*bipartite**graph*K 2,n−5 (see (2) ) with parts B and ... Remove a maximal set*of*edge disjoint*quadrilaterals*from E(G 1 ) and include them to P. The remaining*graph**of*the uncovered edges, G 2 , is*quadrilateral*-free. ...##
###
Page 1673 of Mathematical Reviews Vol. , Issue 2000c
[page]

2000
*
Mathematical Reviews
*

We study several problems related to such

*bipartite**embeddings*.” 2000c:05048 2000c:05045 05C10 Abu-Sbeih, Moh’d Z. (SAR-UPAM; Dhahran) Diagonalizable*embedding**of*composition*graphs*. ... (E-UPMAT; Madrid)*Bipartite**embeddings**of*trees in the plane. (English summary) Discrete Appl. Math. 93 (1999), no. 2-3, 141-148. Summary: “In this paper we consider the following*embedding*problem. ...##
###
Self-dual embeddings of complete bipartite graphs

1992
*
Journal of combinatorial theory. Series B (Print)
*

In this paper we examine self-dual

doi:10.1016/0095-8956(92)90056-4
fatcat:6mnkxinrejhgrcc3gys4z3ja64
*embeddings**of*the complete*bipartite**graph*K", on both orientable and nonorientable surfaces. ... We show by construction that these necessary conditions are sufficient, except that there is no orientable self-dual*embedding**of*K6,6. 0 ... ACKNOWLEDGMENT The authors thank Richard Wilson for the*embedding**of*Kp dual to K6,6 ...##
###
Page 45 of Mathematical Reviews Vol. , Issue 92a
[page]

1992
*
Mathematical Reviews
*

A

*quadrilateral**embedding**of*a*graph*G with 2n vertices in a closed surface S is called diagonalizable if there exists a set*of*n*quadrilaterals**of*the*embedding*and a choice*of*diagonal in each*of*these ... It seems that determining whether an arbitrary*graph*G admits a diagonalizable*quadrilateral**embedding*is a difficult problem. ...
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