A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Book Embeddings of Nonplanar Graphs with Small Faces in Few Pages
[article]

2022
*
arXiv
*
pre-print

For planar

arXiv:2003.07655v2
fatcat:u547yi6d7jbhdgj7omt2ia55xu
*graphs*, a fundamental result is due to Yannakakis, who proposed an algorithm to compute*embeddings**of*planar*graphs**in**books**with*four*pages*. ... An*embedding**of*a*graph**in*a*book*, called*book**embedding*, consists*of*a linear ordering*of*its vertices along the spine*of*the*book*and an assignment*of*its edges to the*pages**of*the*book*, so that no two ... We also thank the useful comments*of*the anonymous referees*of*this paper;*in*particular, we acknowledge one referee for suggesting us to explore the relationship between k-framed and k-map*graphs*. ...##
###
The book thickness of a graph

1979
*
Journal of combinatorial theory. Series B (Print)
*

A

doi:10.1016/0095-8956(79)90021-2
fatcat:h3uxe6q3gbb5vciiekp7tajzm4
*graph*G has*book*thickness bt(G) < 2 if and only if it is a subgraph*of*a hamiltonian planar*graph*, but we conjecture that there are planar*graphs**with*arbitrarily high*book*thickness. ... The*book*thickness bt(G)*of*a*graph*G is defined, its basic properties are delineated, and relations are given*with*other invariants such as thickness, genus, and chromatic number. ... Then a*graph*H is dispersable if there is a*book**embedding**of*H*in*a*book**with*A(H)*pages*and an edge-coloring*of*H*with*Since B is dispersable, let (3 be a*book**embedding**of*B*in*A(B)*pages*and let c ...##
###
Planarizing Graphs - A Survey and Annotated Bibliography

2001
*
Journal of Graph Algorithms and Applications
*

Given a finite, undirected, simple

doi:10.7155/jgaa.00032
fatcat:zftlx3a5jnesxff5hjymjewp5u
*graph*G, we are concerned*with*operations on G that transform it into a planar*graph*. ... We give a survey*of*results about such operations and related*graph*parameters. ... The*book*thickness (also called pagenumber )*of*a*graph*G is the smallest number n so that G can be*embedded**in*a*book**with*n*pages*. ...##
###
Computation in Low-Dimensional Geometry and Topology (Dagstuhl Seminar 19352)

2019
*
Dagstuhl Reports
*

The seminar participants investigated problems

doi:10.4230/dagrep.9.8.84
dblp:journals/dagstuhl-reports/LofflerLSC19
fatcat:jvf6v5zuhngi3igvpucn7miqum
*in*: knot theory, trajectory analysis, algorithmic topology, computational geometry*of*curves, and*graph*drawing,*with*an emphasis on how low-dimensional structures ... This report documents the program and the outcomes*of*Dagstuhl Seminar 19352 "Computation*in*Low-Dimensional Geometry and Topology". ... ., isotopic Fréchet) is really at odds*with*finding a "nice" morph. This is because solutions to isotopic Fréchet shrink spiraling parts*of*the curve infinitesimally*small*and then unspiral them. ...##
###
Fine-Grained Location-Free Planarization in Wireless Sensor Networks

2013
*
IEEE Transactions on Mobile Computing
*

The simulation results show that our method produces high-quality planar

doi:10.1109/tmc.2012.57
fatcat:wmtevvq7k5fvdd4n7nnfkonmai
*graphs**with*a*small*stretch factor*in*practical large-scale networks. ...*In*particular, the majority*of*those location-based algorithms [7], [8] are designed under communication models*of*unit disk*graph*(UDG), and a*few*ones [9], [10] make an effort to construct planar*graphs*... ACKNOWLEDGMENTS The authors are grateful for a variety*of*valuable comments from the anonymous reviewers. Dezun Dong ...##
###
Fine-grained location-free planarization in wireless sensor networks

2011
*
2011 Proceedings IEEE INFOCOM
*

The simulation results show that our method produces high-quality planar

doi:10.1109/infcom.2011.5934878
dblp:conf/infocom/DongLLL11
fatcat:ghdcuffg5bcnxaeieqwtsz37xa
*graphs**with*a*small*stretch factor*in*practical large-scale networks. ...*In*particular, the majority*of*those location-based algorithms [7], [8] are designed under communication models*of*unit disk*graph*(UDG), and a*few*ones [9], [10] make an effort to construct planar*graphs*... ACKNOWLEDGMENTS The authors are grateful for a variety*of*valuable comments from the anonymous reviewers. Dezun Dong ...##
###
Graphs, Skeleta and Reconstruction of Polytopes
[article]

2017
*
arXiv
*
pre-print

This is part

arXiv:1710.00118v2
fatcat:6dr36jkjlfhrvbvs2af4zjux5e
*of*a broader story*of*reconstructing*face*lattices from partial information, first considered comprehensively*in*Gr\"unbaum's 1967*book*. ... A renowned theorem*of*Blind and Mani,*with*a constructive proof by Kalai and an efficiency proof by Friedman, shows that the whole*face*lattice*of*a simple polytope can be determined from its*graph*. ... Acknowledgments Thanks to Karim Adiprasito, Joseph Doolittle, Eran Nevo, Isabella Novik, Raman Sanyal, Hailun Zheng and Günter Ziegler for close reading*of*a draft and useful comments. ...##
###
Beyond-Planar Graphs: Combinatorics, Models and Algorithms (Dagstuhl Seaminar 19092)

2019
*
Dagstuhl Reports
*

algorithms for so-called beyond-planar

doi:10.4230/dagrep.9.2.123
dblp:journals/dagstuhl-reports/Hong0PT19
fatcat:pvtbranvp5fwfkaul2nlmb6m4e
*graphs*, i.e., non-planar*graphs*that admit a drawing*with*topological constraints such as specific types*of*crossings, or*with*some forbidden crossing patterns. ... This report documents the program and the outcomes*of*Dagstuhl Seminar 19092 "Beyond-Planar*Graphs*: Combinatorics, Models and Algorithms" which brought together 36 researchers*in*the areas*of**graph*theory ... We thank Günter Rote and Martin Gronemann for asking interesting questions that led to some*of*this research. ...##
###
Graph Theory with Applications

1977
*
Operational Research Quarterly (1970-1977)
*

This

doi:10.2307/3008805
fatcat:plgnmnhvpbdzze5sxwmgubxgae
*book*is intended as an introduction to*graph*theory. ... Appendix I11 includes a selection*of*interesting*graphs**with*special properties. These may prove to be useful*in*testing new conjectures. ... A plane*graph**with*six*faces*Proof Consider an*embedding*G*of*G on the sphere; such an*embedding*exists by virtue*of*theorem 9.2. ...##
###
Orthogonal Graph Drawing
[chapter]

2001
*
Lecture Notes in Computer Science
*

Let F be the set

doi:10.1007/3-540-44969-8_6
fatcat:nvlgt2hrm5gy5dav2bkoqm27nm
*of**faces**in*this fixed*embedding*,*with*f 0 being the exterior*face*. ... Fig. 6 . 3 . 63 Angles around a vertex*in*a drawing. Fig . 6.4. A family*of**graphs**with**small*angular resolution. ... This situation is modeled by inequalities (6.16.3)*with*the help*of*a big constant M . ...##
###
A course in the mathematics of design

1986
*
Computers and Mathematics with Applications
*

The sequence

doi:10.1016/0898-1221(86)90434-7
fatcat:353kkpvcxvhvnoen4mlyeqgr5y
*of*topics is*graph*theory*with*application to planning a floor plan; polyhedra applied to Platonic solids; tilings*of*the plane*with*application to lattice designs; tiling*of*three-dimensional ... space and spacefilling polyhedra; similarity, proportion and the golden mean*with*application to architectural design; transformations; mirrors and symmetry; and vectors applied to analysis*of*polyhedra ... Professor Alan Stewart helped to shape many*of*the ideas*of*the course and has been an able collaborator*in*teaching it each year. ...##
###
Spectral Partitioning, Eigenvalue Bounds, and Circle Packings for Graphs of Bounded Genus

2006
*
SIAM journal on computing (Print)
*

Algorithms, 5 (1984), pp. 391-407] that one can find asymptotically optimal separators on these

doi:10.1137/s0097539705447244
fatcat:tns23gkpmvgwvgrntbmx7olgri
*graphs*if given both the*graph*and an*embedding**of*it onto a low genus surface. ...*In*this paper, we address two long-standing questions about finding good separators*in**graphs**of*bounded genus and degree: 1. It is a classical result*of*Gilbert, Hutchinson, and Tarjan [J. ... I would also like to thank Nathan Dunfield, Phil Bowers, and Ken Stephenson for their guidance on the theory*of*circle packings, and Christopher Mihelich for his help*in*simplifying the proof*of*Lemma ...##
###
Spectral partitioning, eigenvalue bounds, and circle packings for graphs of bounded genus

2004
*
Proceedings of the thirty-sixth annual ACM symposium on Theory of computing - STOC '04
*

Algorithms, 5 (1984), pp. 391-407] that one can find asymptotically optimal separators on these

doi:10.1145/1007352.1007357
dblp:conf/stoc/Kelner04
fatcat:jpelkx3j55f63ps63pwszthiei
*graphs*if given both the*graph*and an*embedding**of*it onto a low genus surface. ...*In*this paper, we address two long-standing questions about finding good separators*in**graphs**of*bounded genus and degree: 1. It is a classical result*of*Gilbert, Hutchinson, and Tarjan [J. ... I would also like to thank Nathan Dunfield, Phil Bowers, and Ken Stephenson for their guidance on the theory*of*circle packings, and Christopher Mihelich for his help*in*simplifying the proof*of*Lemma ...##
###
The contact invariant in sutured Floer homology
[article]

2007
*
arXiv
*
pre-print

We describe an invariant

arXiv:0705.2828v2
fatcat:s5nxwqssyzeadbqeui3san4giu
*of*a contact 3-manifold*with*convex boundary as an element*of*Juh\'asz's sutured Floer homology. ... Our invariant generalizes the contact invariant*in*Heegaard Floer homology*in*the closed case, due to Ozsv\'ath and Szab\'o. This version has some clarifications and new figures. ... We also thank John Etnyre for the discussions which led to the reformulation*of*the contact invariant*in*[HKM2] . ...##
###
A SURVEY OF PROGRESS IN GRAPH THEORY IN THE SOVIET UNION

1970
*
Annals of the New York Academy of Sciences
*

The best Sovic work has been concerned

doi:10.1111/j.1749-6632.1970.tb56496.x
fatcat:cbb5x22w2farrnw5sijyovn66i
*with*bounds on numerical indices associated*with**graphs*, properties*of*algebraic stvuctures associated*with**graphs*, and operations on*graphs*. ... use*of**graphs*for modeling*in*social sciences. ... Papers*of*the second type deal*with*questions*of*either*embedding*a given*graph**in*a*graph**of*some special type or*embedding*metrics*in**graphs**of*a certain tyl)L-. ...
« Previous

*Showing results 1 — 15 out of 78 results*