Lower bounds for the number of edge-crossings over the spine in a topological book embedding of a graph

Hikoe Enomoto, Miki Shimabara Miyauchi, Katsuhiro Ota

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

In a topological book embedding of a graph, the graph is drawn in a topological book by placing the vertices along the spine of the book and drawing the edges in the pages; edges are allowed to cross the spine. Earlier results show that every graph having n vertices and m edges can be embedded into a 3-page book with at most O(m log n) edge-crossings over the spine. This paper presents lower bounds on the number of edge-crossings over the spine for a variety of graphs. These bounds show that the upper bound O(m log n) is essentially best possible.

Original languageEnglish
Pages (from-to)149-155
Number of pages7
JournalDiscrete Applied Mathematics
Volume92
Issue number2-3
Publication statusPublished - 1999 Jun

Fingerprint

Book Embedding
Spine
Lower bound
Graph in graph theory
Upper bound

Keywords

  • Book embedding
  • Edge crossing
  • Topological book embedding

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Lower bounds for the number of edge-crossings over the spine in a topological book embedding of a graph. / Enomoto, Hikoe; Miyauchi, Miki Shimabara; Ota, Katsuhiro.

In: Discrete Applied Mathematics, Vol. 92, No. 2-3, 06.1999, p. 149-155.

Research output: Contribution to journalArticle

@article{c003367e77334f5395c2ecd748553369,
title = "Lower bounds for the number of edge-crossings over the spine in a topological book embedding of a graph",
abstract = "In a topological book embedding of a graph, the graph is drawn in a topological book by placing the vertices along the spine of the book and drawing the edges in the pages; edges are allowed to cross the spine. Earlier results show that every graph having n vertices and m edges can be embedded into a 3-page book with at most O(m log n) edge-crossings over the spine. This paper presents lower bounds on the number of edge-crossings over the spine for a variety of graphs. These bounds show that the upper bound O(m log n) is essentially best possible.",
keywords = "Book embedding, Edge crossing, Topological book embedding",
author = "Hikoe Enomoto and Miyauchi, {Miki Shimabara} and Katsuhiro Ota",
year = "1999",
month = "6",
language = "English",
volume = "92",
pages = "149--155",
journal = "Discrete Applied Mathematics",
issn = "0166-218X",
publisher = "Elsevier",
number = "2-3",

}

TY - JOUR

T1 - Lower bounds for the number of edge-crossings over the spine in a topological book embedding of a graph

AU - Enomoto, Hikoe

AU - Miyauchi, Miki Shimabara

AU - Ota, Katsuhiro

PY - 1999/6

Y1 - 1999/6

N2 - In a topological book embedding of a graph, the graph is drawn in a topological book by placing the vertices along the spine of the book and drawing the edges in the pages; edges are allowed to cross the spine. Earlier results show that every graph having n vertices and m edges can be embedded into a 3-page book with at most O(m log n) edge-crossings over the spine. This paper presents lower bounds on the number of edge-crossings over the spine for a variety of graphs. These bounds show that the upper bound O(m log n) is essentially best possible.

AB - In a topological book embedding of a graph, the graph is drawn in a topological book by placing the vertices along the spine of the book and drawing the edges in the pages; edges are allowed to cross the spine. Earlier results show that every graph having n vertices and m edges can be embedded into a 3-page book with at most O(m log n) edge-crossings over the spine. This paper presents lower bounds on the number of edge-crossings over the spine for a variety of graphs. These bounds show that the upper bound O(m log n) is essentially best possible.

KW - Book embedding

KW - Edge crossing

KW - Topological book embedding

UR - http://www.scopus.com/inward/record.url?scp=0004321910&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0004321910&partnerID=8YFLogxK

M3 - Article

VL - 92

SP - 149

EP - 155

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 2-3

ER -