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 |
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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 journal › Article
}
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 -