Dot product representations of planar graphs

被引：0
|
作者：
Kang, Ross J. [1 ]
Lovasz, Laszlo [2 ]
Muller, Tobias
Scheinerman, Edward R.
机构：
[1] Univ Durham, Durham DH1 3HP, England
[2] Eotvos Lorand Univ, H-1364 Budapest, Hungary
来源：
ELECTRONIC JOURNAL OF COMBINATORICS | 2011年 / 18卷 / 01期
基金：
欧洲研究理事会; 英国工程与自然科学研究理事会;
关键词：
EUCLIDEAN SPACES; EMBEDDINGS;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A graph G is a k-dot product graph if there exists a vector labelling u : V (G) -> R(k) such that u(i)(T)u(j) >= 1 if and only if ij is an element of E(G). Fiduccia, Scheinerman, Trenk and Zito [Discrete Math., 1998] asked whether every planar graph is a 3-dot product graph. We show that the answer is "no". On the other hand, every planar graph is a 4-dot product graph. We also answer the corresponding questions for planar graphs of prescribed girth and for outerplanar graphs.
引用
收藏
页数：14
相关论文
共 50 条
  • [31] Planar Graphs Have 1-string Representations
    Jérémie Chalopin
    Daniel Gonçalves
    Pascal Ochem
    Discrete & Computational Geometry, 2010, 43 : 626 - 647
  • [32] Planar Graphs Have 1-string Representations
    Chalopin, Jeremie
    Goncalves, Daniel
    Ochem, Pascal
    DISCRETE & COMPUTATIONAL GEOMETRY, 2010, 43 (03) : 626 - 647
  • [33] Edge-weighted contact representations of planar graphs
    1600, Brown University (17):
  • [34] An optimal algorithm for product structure in planar graphs
    Bose, Prosenjit
    Morin, Pat
    Odak, Saeed
    arXiv, 2022,
  • [35] A Fast Algorithm for the Product Structure of Planar Graphs
    Morin, Pat
    ALGORITHMICA, 2021, 83 (05) : 1544 - 1558
  • [36] A Fast Algorithm for the Product Structure of Planar Graphs
    Pat Morin
    Algorithmica, 2021, 83 : 1544 - 1558
  • [37] Graph Matching Based on Dot Product Representation of Graphs
    Tang, Jin
    Jiang, Bo
    Luo, Bin
    GRAPH-BASED REPRESENTATIONS IN PATTERN RECOGNITION, 2011, 6658 : 175 - 184
  • [38] Statistical inference on random dot product graphs: A survey
    Athreya, Avanti
    Fishkind, Donniell E
    Tang, Minh
    Priebe, Carey E
    Park, Youngser
    Vogelstein, Joshua T.
    Levin, Keith
    Lyzinski, Vince
    Qin, Yichen
    Sussman, Daniel L
    Journal of Machine Learning Research, 2018, 18 : 1 - 92
  • [39] Statistical Inference on Random Dot Product Graphs: a Survey
    Athreya, Avanti
    Fishkind, Donniell E.
    Minh Tang
    Priebe, Carey E.
    Park, Youngser
    Vogelstein, Joshua T.
    Levin, Keith
    Lyzinski, Vince
    Qin, Yichen
    Sussman, Daniel L.
    JOURNAL OF MACHINE LEARNING RESEARCH, 2018, 18
  • [40] Optimal Bayesian estimation for random dot product graphs
    Xie, Fangzheng
    Xu, Yanxun
    BIOMETRIKA, 2020, 107 (04) : 875 - 889
12345