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Queue Layouts of Planar 3-Trees

Jawaherul Md. Alam, Michael A. Bekos, Martin Gronemann, Michael Kaufmann, Sergey Pupyrev
<span title="2020-03-23">2020</span> <i title="Springer Science and Business Media LLC"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qhi3z76be5c5xeihac5cyiid3m" style="color: black;">Algorithmica</a> </i> &nbsp;
In this paper, we continue the study of the queue number of planar 3-trees, which form a well-studied subclass of planar graphs.  ...  We also show that there exist planar 3-trees whose queue number is at least four. Notably, this is the first example of a planar graph with queue number greater than three.  ...  To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00453-020-00697-4">doi:10.1007/s00453-020-00697-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/h3pc36ptwvg6tpillzfezsuyqy">fatcat:h3pc36ptwvg6tpillzfezsuyqy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200509120334/https://link.springer.com/content/pdf/10.1007/s00453-020-00697-4.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/7d/9f/7d9f7e43818c8f65d8ce819fcd265635b3fcb000.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00453-020-00697-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Queue Layouts of Planar 3-Trees [article]

Jawaherul Md. Alam, Michael A. Bekos, Martin Gronemann, Michael Kaufmann, Sergey Pupyrev
<span title="2018-09-06">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The queue number of G is the minimum number of queues required by any queue layout of G. In this paper, we continue the study of the queue number of planar 3-trees.  ...  We also show that there exist planar 3-trees, whose queue number is at least four; this is the first example of a planar graph with queue number greater than three.  ...  There exist planar 3-trees that have queue number at least 4. Conclusions In this work, we presented improved bounds on the queue number of planar 3-trees.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1808.10841v2">arXiv:1808.10841v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/efyxjytjrza6bngckrxkfz57k4">fatcat:efyxjytjrza6bngckrxkfz57k4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200825224044/https://arxiv.org/pdf/1808.10841v2.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/45/6e/456eb5ae34e22014a8550664297e3f070394546a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1808.10841v2" 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>

Queue Layouts, Tree-Width, and Three-Dimensional Graph Drawing [chapter]

David R. Wood
<span title="">2002</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;
The minimum number of queues in a queue layout of a graph is its queue-number. Let be an Ò-vertex member of a proper minor-closed family of graphs (such as a planar graph).  ...  A queue layout consists of a linear order of the vertices of a graph, and a partition of the edges into queues, such that no two edges in the same queue are nested with respect to .  ...  That is, graphs of bounded tree-width have bounded queue-number, and hence have three-dimensional drawings with linear volume.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-36206-1_31">doi:10.1007/3-540-36206-1_31</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mgvakktkh5dc7jdvby4oqnjyly">fatcat:mgvakktkh5dc7jdvby4oqnjyly</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190228114733/http://pdfs.semanticscholar.org/916c/a612410349920bc5d172202b54e6483fd99b.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/91/6c/916ca612410349920bc5d172202b54e6483fd99b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-36206-1_31"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Stack and Queue Layouts of Directed Acyclic Graphs: Part I

Lenwood S. Heath, Sriram V. Pemmaraju, Ann N. Trenk
<span title="">1999</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7dys7zoberdktmxyjciuy5bnse" style="color: black;">SIAM journal on computing (Print)</a> </i> &nbsp;
In Section 2, we examine stack layouts of tree dags and unicyclic dags. In Section 3, we examine the queue layouts of tree dags and unicyclic dags.  ...  We also give forbidden subgraph characterizations of 1-queue tree dags and 1-queue cycle dags. In the companion paper 5], we develop algorithmic results for stack and queue layouts of dags.  ...  A 3-queue layout ofŨ is obtained by placing a 2-queue layout of T 1 to the left of a 2-queue layout ofT 2 and then assigning the two arcs inC, incident on u, to a third queue.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/s0097539795280287">doi:10.1137/s0097539795280287</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bvdba6xkfbeqrgikapiw2di2pe">fatcat:bvdba6xkfbeqrgikapiw2di2pe</a> </span>
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On Mixed Linear Layouts of Series-Parallel Graphs [article]

Patrizio Angelini and Michael A. Bekos and Philipp Kindermann and Tamara Mchedlidze
<span title="2020-08-25">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Recently, Pupyrev disproved this conjectured by demonstrating a planar partial 3-tree that does not admit a 1-stack 1-queue layout.  ...  In 1992, Heath and Rosenberg conjectured that every planar graph admits a mixed 1-stack 1-queue layout.  ...  This improves upon the partial planar 3-tree negative example by Pupyrev [24] . Note that 2-trees admit both 2-stack layouts and 3-queue layouts [25] . Preliminaries.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2008.10475v2">arXiv:2008.10475v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bcqzavoinnegtl3vk3kzz7whru">fatcat:bcqzavoinnegtl3vk3kzz7whru</a> </span>
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The Local Queue Number of Graphs with Bounded Treewidth [article]

Laura Merker, Torsten Ueckerdt
<span title="2020-08-12">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Our results imply, inter alia, that the maximum local queue number among planar graphs is either 3 or 4.  ...  A queue layout of a graph G consists of a vertex ordering of G and a partition of the edges into so-called queues such that no two edges in the same queue nest, i.e., have their endpoints ordered in an  ...  The lower bound of 4 is obtained by a planar 3-tree. Alam et al. [4] also show that every planar 3-tree admits a 5-queue layout.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2008.05392v1">arXiv:2008.05392v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/my4zz5s5dvau3a3ifbbao5xfwm">fatcat:my4zz5s5dvau3a3ifbbao5xfwm</a> </span>
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Planar Graphs of Bounded Degree have Constant Queue Number [article]

Michael A. Bekos, Henry Förster, Martin Gronemann, Tamara Mchedlidze, Fabrizio Montecchiani, Chrysanthi Raftopoulou, Torsten Ueckerdt
<span title="2019-08-09">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The queue number of a graph is the minimum number of queues required by any of its queue layouts.  ...  A queue layout of a graph consists of a linear order of its vertices and a partition of its edges into queues, so that no two independent edges of the same queue are nested.  ...  Wood for pointing out an issue in an earlier version of this paper and the anonymous referees of both the journal and the conference version of this paper for their valuable comments and suggestions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1811.00816v3">arXiv:1811.00816v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2cd65psucfe6znckdq7yps4bdm">fatcat:2cd65psucfe6znckdq7yps4bdm</a> </span>
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Improved Bounds for Track Numbers of Planar Graphs [article]

Sergey Pupyrev
<span title="2019-10-30">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We prove that every planar graph has track number at most 225 and every planar 3-tree has track number at most 25.  ...  Finally, we investigate leveled planar graphs and tighten bounds on the track number of weakly leveled graphs, Halin graphs, and X-trees.  ...  We thank Jawaherul Alam, Michalis Bekos, Martin Gronemann, and Michael Kaufmann for fruitful initial discussions of the problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.14153v1">arXiv:1910.14153v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4dafhb3rgff5ra3ud6dx5i2kya">fatcat:4dafhb3rgff5ra3ud6dx5i2kya</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200727083616/https://arxiv.org/pdf/1910.14153v1.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] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.14153v1" 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>

Queue Layouts of Graphs with Bounded Degree and Bounded Genus [article]

Vida Dujmović and Pat Morin and David R. Wood
<span title="2019-03-17">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Motivated by the question of whether planar graphs have bounded queue-number, we prove that planar graphs with maximum degree Δ have queue-number O(Δ^2), which improves upon the best previous bound of  ...  As a byproduct we prove that if planar graphs have bounded queue-number, then graphs of Euler genus g have queue-number O(g).  ...  [12] conjectured that every planar graph has bounded queue number. This conjecture has remained open despite much research on queue layouts [3, 5-8, 10-14, 16, 18, 19] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1901.05594v2">arXiv:1901.05594v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/665twqppirgk7dhp7kubxi4gji">fatcat:665twqppirgk7dhp7kubxi4gji</a> </span>
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Book Embeddings of Graph Products [article]

Sergey Pupyrev
<span title="2020-07-29">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The results are obtained via a novel concept of simultaneous stack-queue layouts, which may be of independent interest.  ...  A k-queue layout is defined similarly, except that no two edges in a single set may be nested.  ...  We stress that the result combined with a decomposition theorem for planar graphs [13, 27] (such as one given by Lemma 1) and the fact that the queue number of planar 3-trees is bounded by a constant  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.15102v1">arXiv:2007.15102v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hpjrwfbyvvbtbg54hbes3wdbhe">fatcat:hpjrwfbyvvbtbg54hbes3wdbhe</a> </span>
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On the queue-number of graphs with bounded tree-width [article]

Veit Wiechert
<span title="2016-08-22">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The minimum number of queues needed in a queue layout of a graph is called its queue-number. We show that for each k≥1, graphs with tree-width at most k have queue-number at most 2^k-1.  ...  Already in the case k=2 this is an improvement to existing results and solves a problem of Rengarajan and Veni Madhavan, namely, that the maximal queue-number of 2-trees is equal to 3.  ...  However, now with Theorem 1 we even get that planar 3-trees (and more generally partial 3-trees) have queue-number at most 7. Track layouts.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1608.06091v1">arXiv:1608.06091v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gwibverdkreorgcv6wknavdmwq">fatcat:gwibverdkreorgcv6wknavdmwq</a> </span>
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Layout of Graphs with Bounded Tree-Width

Vida Dujmovic, Pat Morin, David R. Wood
<span title="">2005</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7dys7zoberdktmxyjciuy5bnse" style="color: black;">SIAM journal on computing (Print)</a> </i> &nbsp;
This result provides renewed hope for the positive resolution of a number of open problems in the theory of queue layouts. (3) It is proved that graphs of bounded tree-width have three-dimensional drawings  ...  The minimum number of queues in a queue layout of a graph is its queue-number.  ...  It is possible, however, that planar graphs have unbounded queue-number, yet have say O(n 1/3 ) × O(n 1/3 ) × O(n 1/3 ) drawings. 2. 2 . 2 Tree-Partitions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/s0097539702416141">doi:10.1137/s0097539702416141</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lwrkyo5q7jczbel7ht6kjrgqem">fatcat:lwrkyo5q7jczbel7ht6kjrgqem</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20070418022435/http://cg.scs.carleton.ca/~morin/publications/gd/treewidth-sicomp.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/b0/db/b0db6bf7b451c2a5f29e69be3b6f35a8133badcd.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/s0097539702416141"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Stacks, Queues and Tracks: Layouts of Graph Subdivisions

Vida Dujmović, David R. Wood
<span title="2005-01-01">2005</span> <i title="Centre pour la Communication Scientifique Directe (CCSD)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/aagtqr2vajamvduhte7kigeygi" style="color: black;">Discrete Mathematics &amp; Theoretical Computer Science</a> </i> &nbsp;
\par This paper studies stack, queue, and track layouts of graph subdivisions. It is known that every graph has a 3-stack subdivision.  ...  This result reduces the question of whether queue-number is bounded by stack-number to whether 3-stack graphs have bounded queue number.  ...  Thanks to Franz Brandenburg and Ulrik Brandes for pointing out the connection to double-ended queues. Thanks to Ferran Hurtado and Prosenjit Bose for graciously hosting the second author.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.46298/dmtcs.346">doi:10.46298/dmtcs.346</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/olvfxbq3ozgapla2gms6we5srm">fatcat:olvfxbq3ozgapla2gms6we5srm</a> </span>
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Graph Layouts via Layered Separators [article]

Vida Dujmovic
<span title="2013-02-01">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The queue-number (track-number) of a graph G, is the minimum k such that G has a k-queue (k-track) layout.  ...  A k-queue layout of a graph consists of a total order of the vertices, and a partition of the edges into k sets such that no two edges that are in the same set are nested with respect to the vertex ordering  ...  The minimum number of queues in a queue layout of a graph is its queue-number.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1302.0304v1">arXiv:1302.0304v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2z54id74jrhzbbj7dws6f7nnse">fatcat:2z54id74jrhzbbj7dws6f7nnse</a> </span>
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Graph layouts via layered separators

Vida Dujmović
<span title="">2015</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/g6u5fful5vcr3a7gppc6y47el4" style="color: black;">Journal of combinatorial theory. Series B (Print)</a> </i> &nbsp;
The queue-number (track-number) of a graph G, is the minimum k such that G has a k-queue (k-track) layout.  ...  A k-queue layout of a graph consists of a total order of the vertices, and a partition of the edges into k sets such that no two edges that are in the same set are nested with respect to the vertex ordering  ...  The minimum number of queues in a queue layout of a graph is its queue-number.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jctb.2014.07.005">doi:10.1016/j.jctb.2014.07.005</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pqta4or42vgofkwb7wexa3o2ym">fatcat:pqta4or42vgofkwb7wexa3o2ym</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150427234309/http://cglab.ca/~vida/pubs/papers/layered.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/92/6f/926ff93561753e1d9d6ee2a2a13aadcb02246e2b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jctb.2014.07.005"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>
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