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Improved upper bounds on the area required to embed arbitrary graphs

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Dunne, Paul E. (1983) Improved upper bounds on the area required to embed arbitrary graphs. Coventry, UK: University of Warwick. Department of Computer Science. (Department of Computer Science Research Report). (Unpublished)

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Abstract

We prove that any n-vertex graph of maximum degree r(r=3 or 4) can be embedded in a square grid of area Ar(n), where:

A3(n) ≤ n2/4 + O (n3/2)
A3(n) ≤ n2 + O (n3/2)

Item Type: Report
Subjects: Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions: Faculty of Science, Engineering and Medicine > Science > Computer Science
Library of Congress Subject Headings (LCSH): Graph theory
Series Name: Department of Computer Science Research Report
Publisher: University of Warwick. Department of Computer Science
Place of Publication: Coventry, UK
Official Date: December 1983
Dates:
DateEvent
December 1983Completion
Number: Number 55
Number of Pages: 9
DOI: CS-RR-055
Institution: University of Warwick
Theses Department: Department of Computer Science
Status: Not Peer Reviewed
Publication Status: Unpublished
Reuse Statement (publisher, data, author rights): P.E.&nbsp;Dunne, &ldquo;A Result on k-valent Graphs and its Application to a Graph Embedding Problem&rdquo;, <i>Acta Informatica</i> <b>24</b>, pp.&nbsp;447-458 (1987)
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