An 0(mn) Algorithm for Embedding Graphs into a 3-Page Book

Miki SHIMABARA MIYAUCHI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E77-A   No.3   pp.521-526
Publication Date: 1994/03/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on the 6th Karuizawa Workshop on Circuits and Systems)
Category: Graphs, Networks and Matroids
Keyword: 
graphs,  algorithms,  data structures and computational complexity,  VLSI design technology,  

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Summary: 
This paper studies the problem of embedding a graph into a book with nodes on a line along the spine of the book and edges on the pages in such a way that no edge crosses another. Atneosen as well as Bernhart and Kainen has shown that every graph can be embedded into a 3-page book when each edge can be embedded in more than one page. The time complexity of Bernhart and Kainen's method is Ω(ν(G)), where ν(G) is the crossing number of a graph G. A new 0(mn) algorithm is derived in this paper for embedding a graph G=(V, E), where m=│E│ and n= │V│ . The number of points at which edges cross over the spine in embedding a complete graph into a 3-page book is also investigated.