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.
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页数：14
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