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A Sublinear Bound on the Page Number of Upward Planar Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2022 The page number of a directed acyclic graph $G$ is the minimum $k$ for which there is a topological ordering of $G$ and a $k$-coloring of the edges such that no two edges of the same color cross, i.e., have alternating endpoints along the topological ordering. We address the long-standing open problem asking for the largest page number among all upward
Paul Jungeblut +2 more
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The mixed page number of graphs
Theoretical Computer Science, 2022 A linear layout of a graph typically consists of a total vertex order, and a partition of the edges into sets of either non-crossing edges, called stacks, or non-nested edges, called queues. The stack (queue) number of a graph is the minimum number of required stacks (queues) in a linear layout.
Jawaherul Md. Alam +4 more
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Don't use the page number, but a pointer to it [PDF]
Proceedings of the 23rd annual international symposium on Computer architecture, 1996 Most newly announced high performance microprocessors support 64-bit virtual addresses and the width of physical addresses is also growing. As a result, the size of the address tags in the L1 cache is increasing. The impact of on chip area is particularly dramatic when small block sizes are used.
André Seznec
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On the Page Number of Upward Planar Directed Acyclic Graphs [PDF]
Journal of Graph Algorithms and Applications, 2012 In this paper we study the page number of upward planar directed acyclic graphs. We prove that: (1) the page number of any n-vertex upward planar triangulation G whose every maximal 4-connected component has page number k is at most min {O(klogn),O(2k)}; (2) every upward planar triangulation G with $o(\frac{n}{\log n})$ diameter has o(n) page ...
Frati Fabrizio +2 more
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Local and Union Page Numbers [PDF]
International Symposium Graph Drawing and Network Visualization, 2019 We introduce the novel concepts of local and union book embeddings, and, as the corresponding graph parameters, the local page number ${\rm pn}_\ell(G)$ and the union page number ${\rm pn}_u(G)$. Both parameters are relaxations of the classical page number ${\rm pn}(G)$, and for every graph $G$ we have ${\rm pn}_\ell(G) \leq {\rm pn}_u(G) \leq {\rm pn}(
Torsten Ueckerdt, Laura Merker
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On the page-number of a circulant graph
AKCE International Journal of Graphs and CombinatoricsThe page-number of a graph G, denoted by p(G), is the minimum k such that G has an embedding in a k-book. The circulant graph C(m, n) is such a graph that its vertex set is [Formula: see text] and edge set is [Formula: see text], where m, n are positive ...
Xiaoyuan Dong, Dengju Ma
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Electronic Notes in Discrete Mathematics, 2005 Abstract In this paper we deal with the page number of partially ordered sets (posets). We provide a lower bound in the terms of the jump number and then study posets with page number 2.
Maciej M. Sysło, Anna Beata Kwiatkowska
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Journal of Formalized Reasoning, 2008 We discuss the formalization, in the Matita Interactive Theorem Prover, of a few elementary results in number theory about the Moebius mu function and the Euler phi function.
Cristian Armentano, Andrea Asperti
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Iranian Journal of Public Health, 2016 Background: Citation metrics and total publications in a field has become the gold standard for rating researchers and viability of a field. Hence, stimulating demand for citation has led to a search for useful strategies to improve performance metric ...
Abubakar AHMED +4 more
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