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
N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
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
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U2 - 10.1016/S0166-218X(99)00044-X
DO - 10.1016/S0166-218X(99)00044-X
M3 - Article
AN - SCOPUS:0004321910
VL - 92
SP - 149
EP - 155
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
SN - 0166-218X
IS - 2-3
ER -