On linear layouts of graphs

被引:1
|
作者
Dujmovic, V [1 ]
Wood, DR
机构
[1] McGill Univ, Sch Comp Sci, Montreal, PQ, Canada
[2] Carleton Univ, Sch Comp Sci, Ottawa, ON K1S 5B6, Canada
[3] Charles Univ Prague, Dept Appl Math, CR-11800 Prague, Czech Republic
关键词
graph layout; graph drawing; stack layout; queue layout; arch layout; book embedding; queue-number; stack-number; page-number; book-thickness;
D O I
暂无
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
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 edges into k sets of pairwise non-crossing (respectively, non-nested, non-disjoint) edges. Motivated by numerous applications, stack layouts (also called book embeddings) and queue layouts are widely studied in the literature, while this is the first paper to investigate arch layouts. Our main result is a characterisation of k-arch graphs as the almost (k+1)-colourable graphs; that is, the graphs G with a set S of at most k vertices, such that G\S is ( k+1)-colourable. In addition, we survey the following fundamental questions regarding each type of layout, and in the case of queue layouts, provide simple proofs of a number of existing results. How does one partition the edges given a fixed ordering of the vertices? What is the maximum number of edges in each type of layout? What is the maximum chromatic number of a graph admitting each type of layout? What is the computational complexity of recognising the graphs that admit each type of layout? A comprehensive bibliography of all known references on these topics is included.
引用
收藏
页码:339 / 357
页数:19
相关论文
共 50 条
  • [1] Linear layouts of weakly triangulated graphs
    Mukhopadhyay, Asish
    Rao, S. V.
    Pardeshi, Sidharth
    Gundlapalli, Srinivas
    [J]. DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2016, 8 (03)
  • [2] Linear layouts measuring neighbourhoods in graphs
    Gurski, Frank
    [J]. DISCRETE MATHEMATICS, 2006, 306 (15) : 1637 - 1650
  • [3] Linear Layouts of Weakly Triangulated Graphs
    Mukhopadhyay, Asish
    Rao, S. V.
    Pardeshi, Sidharth
    Gundlapalli, Srinivas
    [J]. ALGORITHMS AND COMPUTATION, WALCOM 2014, 2014, 8344 : 322 - 336
  • [4] On mixed linear layouts of series-parallel graphs
    Angelini, Patrizio
    Bekos, Michael A.
    Kindermann, Philipp
    Mchedlidze, Tamara
    [J]. THEORETICAL COMPUTER SCIENCE, 2022, 936 : 129 - 138
  • [5] Parameterized Algorithms for Linear Layouts of Graphs with Respect to the Vertex Cover Number
    Liu, Yunlong
    Li, Yixuan
    Huang, Jingui
    [J]. COMBINATORIAL OPTIMIZATION AND APPLICATIONS, COCOA 2021, 2021, 13135 : 553 - 567
  • [6] Track layouts of graphs
    Dujmovic, V
    Pór, A
    Wood, DR
    [J]. DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, 2004, 6 (02): : 497 - 521
  • [7] VLSI layouts of complete graphs and star graphs
    Yeh, CH
    Parhami, B
    [J]. INFORMATION PROCESSING LETTERS, 1998, 68 (01) : 39 - 45
  • [8] Enumerating grid layouts of graphs
    Damaschke, Peter
    [J]. Journal of Graph Algorithms and Applications, 2020, 24 (03) : 433 - 460
  • [9] FLOORPLANS, PLANAR GRAPHS, AND LAYOUTS
    WIMER, S
    KOREN, I
    CEDERBAUM, I
    [J]. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1988, 35 (03): : 267 - 278
  • [10] Rectangular Layouts and Contact Graphs
    Buchsbaum, Adam L.
    Gansner, Emden R.
    Procopiuc, Cecilia M.
    Venkatasubramanian, Suresh
    [J]. ACM TRANSACTIONS ON ALGORITHMS, 2008, 4 (01)