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Page 9207 of Mathematical Reviews Vol. , Issue 2004k [page]

<span title="">2004</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
M. (6-IIS; Bangalore) ; Ramesh, H. (6-IIS; Bangalore) Lower bounds for embedding graphs into graphs of smaller characteristic.  ...  Further, we will also give an alternative proof for lower bounding the distortion when probabilistically embedding expander graphs into tree metrics.  ... 
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A Heawood-type result for the algebraic connectivity of graphs on surfaces [article]

Pedro Freitas
<span title="2001-09-24">2001</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
As an application of these results and techniques, we obtain a lower bound for the genus of Ramanujan graphs.  ...  We also present some bounds for the asymptotic behaviour of a(G) for certain classes of graphs as the number of vertices goes to infinity.  ...  A lower bound for the genus of Ramanujan graphs It is possible to use the bounds in Corollary 3.2 to obtain estimates for the genus of a given graph, provided one has a lower bound for a(G) -this is actually  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0109191v1">arXiv:math/0109191v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sldd75uwcjagtn3mdjj7kgkbku">fatcat:sldd75uwcjagtn3mdjj7kgkbku</a> </span>
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Lower Bounds for Embedding into Distributions over Excluded Minor Graph Families [chapter]

Douglas E. Carroll, Ashish Goel
<span title="">2004</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We show that this same lower bound holds for embeddings into distributions over any minor excluded family.  ...  We also extend a result of Alon et al. [1] by showing that for any k, planar graphs cannot be embedded into distributions over treewidth-k graphs with better than Ω(log n) distortion.  ...  We would also like to thank Elias Koutsoupias for valuable discussions, and Adam Meyerson and Shailesh Vaya for helpful comments on previous drafts.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-30140-0_15">doi:10.1007/978-3-540-30140-0_15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5ihzwtzh6jbq3jarj3ea6dtrna">fatcat:5ihzwtzh6jbq3jarj3ea6dtrna</a> </span>
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The genus crossing number

Bojan Mohar
<span title="2009-09-26">2009</span> <i title="University of Primorska Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gvgtrk4iyvatbibvfwr3uifrji" style="color: black;">Ars Mathematica Contemporanea</a> </i> &nbsp;
It remains an open question if the genus crossing number can be strictly smaller than the degenerate crossing number of Pach and Tóth.  ...  These facts follow from the proof that the genus crossing number is indeed equal to the non-orientable genus of the graph.  ...  This yields the lower bound. To prove the upper bound, let H be a maximal outerplanar graph of G.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.26493/1855-3974.21.157">doi:10.26493/1855-3974.21.157</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wwh2b4bd2jgjthtqiaklwdyezi">fatcat:wwh2b4bd2jgjthtqiaklwdyezi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190302082456/http://pdfs.semanticscholar.org/a029/cb1242bfbfec31c0b53517b3b2907f9131fd.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a0/29/a029cb1242bfbfec31c0b53517b3b2907f9131fd.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.26493/1855-3974.21.157"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Lower Bounds for Embedding into Distributions over Excluded Minor Graph Families [article]

Douglas E. Carroll, Ashish Goel
<span title="2008-07-29">2008</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We show that this same lower bound holds for embeddings into distributions over any minor excluded family.  ...  We also extend a result of Alon et al by showing that for any k, planar graphs cannot be embedded into distributions over treewidth-k graphs with better than Omega(log n) distortion.  ...  We would also like to thank Elias Koutsoupias for valuable discussions, and Adam Meyerson and Shailesh Vaya for helpful comments on previous drafts.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0807.4582v1">arXiv:0807.4582v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4viasdxsv5fmnlummxn4jl5iqm">fatcat:4viasdxsv5fmnlummxn4jl5iqm</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-0807.4582/0807.4582.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0807.4582v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Expected Crossing Numbers

Bojan Mohar, Tamon Stephen
<span title="">2011</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fhi2xwpnh5gmlgof2idwu5wlgq" style="color: black;">Electronic Notes in Discrete Mathematics</a> </i> &nbsp;
It remains an open question if the genus crossing number can be strictly smaller than the degenerate crossing number of Pach and Tóth.  ...  These facts follow from the proof that the genus crossing number is indeed equal to the non-orientable genus of the graph.  ...  This yields the lower bound. To prove the upper bound, let H be a maximal outerplanar graph of G.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.endm.2011.10.009">doi:10.1016/j.endm.2011.10.009</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hx5yaus7ebg7zhofhrnzwz46si">fatcat:hx5yaus7ebg7zhofhrnzwz46si</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829195128/http://www.sfu.ca/~mohar/Reprints/Inprint/BM07_Preprint_Mohar_GenusCrossingNumber.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/41/ac/41ac934a75ce0a634efda7442f8fc52141349ed5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.endm.2011.10.009"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Expected Crossing Numbers [chapter]

Bojan Mohar, Tamon Stephen
<span title="">2013</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/eigu4bnxqzho5hp4reds2bvswy" style="color: black;">Fields Institute Communications</a> </i> &nbsp;
It remains an open question if the genus crossing number can be strictly smaller than the degenerate crossing number of Pach and Tóth.  ...  These facts follow from the proof that the genus crossing number is indeed equal to the non-orientable genus of the graph.  ...  This yields the lower bound. To prove the upper bound, let H be a maximal outerplanar graph of G.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-00200-2_12">doi:10.1007/978-3-319-00200-2_12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fybo5nvjcnhg3ijlshhz5ultcu">fatcat:fybo5nvjcnhg3ijlshhz5ultcu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829195128/http://www.sfu.ca/~mohar/Reprints/Inprint/BM07_Preprint_Mohar_GenusCrossingNumber.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/41/ac/41ac934a75ce0a634efda7442f8fc52141349ed5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-00200-2_12"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Efficient VLSI layouts for homogeneous product networks

A. Fernandez, K. Efe
<span title="">1997</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5jlmyrayyrdazh5awdlsoec77q" style="color: black;">IEEE transactions on computers</a> </i> &nbsp;
In the literature, lower bounds are generally obtained by computing lower bounds on the bisection width or the crossing number of the network being laid out.  ...  Both methods have the basic limitation that they are applicable only for graphs with bounded vertex degree.  ...  Fernández's contribution to this work was made during the time in which he was at the University of Southwestern Louisiana.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/12.628392">doi:10.1109/12.628392</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kkscicreqna4hdquiwwcimizfi">fatcat:kkscicreqna4hdquiwwcimizfi</a> </span>
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Learning Structural Node Embeddings via Diffusion Wavelets

Claire Donnat, Marinka Zitnik, David Hallac, Jure Leskovec
<span title="">2018</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fqqihtxlu5bvfaqxjyvqcob35a" style="color: black;">Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery &amp; Data Mining - KDD &#39;18</a> </i> &nbsp;
The identification of such roles provides key insight into the organization of networks and can be used for a variety of machine learning tasks.  ...  Nodes residing in different parts of a graph can have similar structural roles within their local network topology.  ...  When the bulk of the eigenvalues leans towards λ N , ∆ (s ) a is closer to e −λ N (i.e., lower bound in Proposition 2).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/3219819.3220025">doi:10.1145/3219819.3220025</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/kdd/DonnatZHL18.html">dblp:conf/kdd/DonnatZHL18</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/a6s64leguvfytfbpqyjqw4rgna">fatcat:a6s64leguvfytfbpqyjqw4rgna</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200822104046/https://arxiv.org/pdf/1710.10321v3.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/9c/e4/9ce4af4671ae1fbd30b5c3641dbd36c78cab1b47.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/3219819.3220025"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Exploring complex networks via topological embedding on surfaces

Tomaso Aste, Ruggero Gramatica, T. Di Matteo
<span title="2012-09-14">2012</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nuk2stxzvvhf7ljciu325kj77m" style="color: black;">Physical Review E</a> </i> &nbsp;
Remarkably, the study of topologically embedded graphs is non-restrictive because any network can be embedded on a surface with sufficiently high genus.  ...  We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties.  ...  Incidentally, Eq.4 provides us with a lower bound for the genus required to embed any network.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreve.86.036109">doi:10.1103/physreve.86.036109</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/23030982">pmid:23030982</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zjltf64ffrfgrkscju46ww3bxy">fatcat:zjltf64ffrfgrkscju46ww3bxy</a> </span>
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Solving large Minimum Vertex Cover problems on a quantum annealer [article]

Elijah Pelofske, Georg Hahn, Hristo N. Djidjev
<span title="2019-05-01">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Quantum annealers can find the optimum solution of such NP-hard problems, given they can be embedded on the hardware.  ...  This paper presents a decomposition algorithm for the minimum vertex cover problem: The algorithm recursively divides an arbitrary problem until the generated subproblems can be embedded and solved on  ...  For D-Wave 2000Q, arbitrary graphs of roughly 65 vertices can be embedded.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1904.00051v3">arXiv:1904.00051v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pbxxf2moezeftmwycobpn2zzj4">fatcat:pbxxf2moezeftmwycobpn2zzj4</a> </span>
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Persona2vec: A Flexible Multi-role Representations Learning Framework for Graphs [article]

Jisung Yoon, Kai-Cheng Yang, Woo-Sung Jung, Yong-Yeol Ahn
<span title="2020-10-21">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Graph embedding techniques, which learn low-dimensional representations of a graph, are achieving state-of-the-art performance in many graph mining tasks.  ...  Most existing embedding algorithms assign a single vector to each node, implicitly assuming that a single representation is enough to capture all characteristics of the node.  ...  Again, in practice, the number of persona edges is much smaller than this upper bound.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.04941v2">arXiv:2006.04941v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/d76pxscjebdnbmafiso2cucalu">fatcat:d76pxscjebdnbmafiso2cucalu</a> </span>
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Lower bounds for graph embeddings and combinatorial preconditioners

Gary L. Miller, Peter C. Richter
<span title="">2004</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tewj77cuufbzbgbk265bb462ga" style="color: black;">Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures - SPAA &#39;04</a> </i> &nbsp;
lower bound for the case in which G is a square mesh.  ...  Often this measure is some combination of the congestion and dilation of an embedding of G into H.  ...  LOWER BOUNDS FOR SPANNERS AND FILLERS In this section, we prove lower bounds for low-characteristic spanners and fillers of sparse graphs, nearly matching the known upper bounds.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1007912.1007929">doi:10.1145/1007912.1007929</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/spaa/MillerR04.html">dblp:conf/spaa/MillerR04</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2kjzdyqwwvcprhdkiijuan7ppi">fatcat:2kjzdyqwwvcprhdkiijuan7ppi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20151016134350/http://www.cs.cmu.edu/~glmiller/Publications/MiRi04.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/65/9c/659c09154609aa8c71deccb93359f7b98775dcff.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1007912.1007929"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

EmbAssi: Embedding Assignment Costs for Similarity Search in Large Graph Databases [article]

Franka Bause, Erich Schubert, Nils M. Kriege
<span title="2022-04-20">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We propose several lower bounds of the graph edit distance obtained from tree metrics reflecting the edit costs, which are combined for effective filtering.  ...  This special case allows embedding the costs of optimal assignments isometrically into ℓ_1 space, rendering efficient indexing possible.  ...  We achieve this by developing tight lower bounds based on assignment costs which are embedded into a vector space for index-based acceleration.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2111.07761v2">arXiv:2111.07761v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2psp3up6bnaynmoxa4eaz2idnu">fatcat:2psp3up6bnaynmoxa4eaz2idnu</a> </span>
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Improved Guarantees for Vertex Sparsification in Planar Graphs [article]

Gramoz Goranci, Monika Henzinger, Pan Peng
<span title="2017-02-03">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Graph Sparsification aims at compressing large graphs into smaller ones while preserving important characteristics of the input graph.  ...  It improves the previous best-known bound of O(k^22^2k) for cut and flow sparsifiers by an exponential factor, and matches an Ω(k^2) lower-bound for this class of graphs.  ...  , which is thus a lower bound for planar graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1702.01136v1">arXiv:1702.01136v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pghxyimrvfgptl7vgq5ubynyai">fatcat:pghxyimrvfgptl7vgq5ubynyai</a> </span>
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