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Discrete Mathematics & Theoretical Computer Science, 2004 A (k,t)-track layout of a graph G consists of a (proper) vertex t-colouring of G, a total order of each vertex colour class, and a (non-proper) edge k-colouring such that between each pair of colour classes no two monochromatic edges cross.
Vida Dujmović +2 more
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Queue Layouts of Graph Products and Powers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 A \emphk-queue layout of a graph G consists of a linear order σ of V(G), and a partition of E(G) into k sets, each of which contains no two edges that are nested in σ .
David R. Wood
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Stacks, Queues and Tracks: Layouts of Graph Subdivisions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 A k-stack layout (respectively, k-queuelayout) of a graph consists of a total order of the vertices, and a partition of the edges into k sets of non-crossing (non-nested) edges with respect to the vertex ordering.
Vida Dujmović, David R. Wood
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Stack and Queue Layouts of Posets [PDF]
SIAM Journal on Discrete Mathematics, 1997 Summary: The stacknumber (queuenumber) of a poset is defined as the stacknumber (queuenumber) of its Hasse diagram viewed as a directed acyclic graph. Upper bounds on the queuenumber of a poset are derived in terms of its jumpnumber, its length, its width, and the queuenumber of its covering graph.
Heath, Lenwood S., Pemmaraju, Sriram V.
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Lazy Queue Layouts of Posets [PDF]
Algorithmica, 2020 AbstractWe investigate the queue number of posets in terms of their width, that is, the maximum number of pairwise incomparable elements. A long-standing conjecture of Heath and Pemmaraju asserts that every poset of width w has queue number at most w. The conjecture has been confirmed for posets of width $$w=2$$ w
Jawaherul Md. Alam +4 more
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Parameterized Algorithms for Queue Layouts [PDF]
Journal of Graph Algorithms and Applications, 2020 An $h$-queue layout of a graph $G$ consists of a linear order of its vertices and a partition of its edges into $h$ sets, called queues, such that no two independent edges of the same queue nest. The minimum $h$ such that $G$ admits an $h$-queue layout is the queue number of $G$.
Sujoy Bhore +3 more
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Process analysis and optimal facility layout planning in manufacturing systems [PDF]
Yugoslav Journal of Operations Research, 2023 In this article, it is emphasized that the process analysis for companies is carried out by using the DISCO process mining program and the results are interpreted and developed.
Ceylan Cemil +3 more
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On Linear Layouts of Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2004 In a total order of the vertices of a graph, two edges with no endpoint in common can be crossing, nested, or disjoint. A k-stack (respectively, k-queue, k-arch) layout of a graph consists of a total order of the vertices, and a partition of the
Vida Dujmović, David R. Wood
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Queue Layouts of Planar 3-Trees [PDF]
Algorithmica, 2018 AbstractA queue layout of a graph G consists of a linear order of the vertices of G and a partition of the edges of G into queues, so that no two independent edges of the same queue are nested. The queue number of graph G is defined as the minimum number of queues required by any queue layout of G.
Alam, Jawaherul Md. +4 more
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Stack and Queue Layouts via Layered Separators [PDF]
Journal of Graph Algorithms and Applications, 2016 It is known that every proper minor-closed class of graphs has bounded stack-number (a.k.a. book thickness and page number). While this includes notable graph families such as planar graphs and graphs of bounded genus, many other graph families are not closed under taking minors.
Dujmović, Vida, Frati, Fabrizio
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