### 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 language | English |
---|---|

Pages (from-to) | 149-155 |

Number of pages | 7 |

Journal | Discrete Applied Mathematics |

Volume | 92 |

Issue number | 2-3 |

Publication status | Published - 1999 Jun |

### Fingerprint

### 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

*Discrete Applied Mathematics*,

*92*(2-3), 149-155.

**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.

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 92, no. 2-3, pp. 149-155.

}

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 -