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The bisection width of cubic graphs

Published online by Cambridge University Press:  17 April 2009

L.H. Clark  and
R.C. Entringer
L.H. Clark
Affiliation:
Department of Mathematics, The University of New Mexico, Albuquerque, NM. 87131United States of America.
R.C. Entringer
Affiliation:
Department of Mathematics, The University of New Mexico, Albuquerque, NM. 87131United States of America.
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Abstract

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For a graph G, define the bisection width bw(G) of G as min { eG(A,B): {A,B} partitions V(G) with ‖A| − |B‖ ≤ 1 } where eG(A, B) denotes the number of edges in G with one end in A and one end in B. We show almost every cubic graph G of order n has bw(G) ≥ n/11 while every such graph has bw(G) ≤ (n + 138)/3. We also show that almost every r-regular graph G of order n has bw(G) ≥ crn where cr → r/4 as r → ∞. Our last result is asymtotically correct.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 3 , June 1989 , pp. 389 - 396
Copyright
Copyright © Australian Mathematical Society 1989

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