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Short disjoint cycles in cubic bridgeless graphs

  • Andreas Brandstädt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 570)

Abstract

The girth g(G) of a finite simple undirected graph G = (V, E) is defined as the minimum length of a cycle in G. We develope a technique which shows the existence of Ω(n1/7) pairwise disjoint cycles of length 0(n6/7) in cubic bridgeless graphs.

As a consequence, for bridgeless graphs with deg v ε 2,3 for all v ε V and ¦v: deg v = 3¦/¦v: deg v = 2¦≥ c > 0 the girth g(G) is bounded by 0(n6/7). Furthermore similarly as for cycles, the existence of many small disjoint subgraphs with k vertices and k + 2 edges is shown. This very technical result is useful in solving the bisection problem (configuring transputer networks) for regular graphs of degree 4 as B. Monien pointed out. Furthermore the existence of many disjoint cycles in such graphs could be also of selfstanding interest.

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References

  1. [Gol 80]
    M.C.Golumbic, Algorithmic Graph Theory, Academic Press 1980Google Scholar
  2. [Hr Mo 90]
    J. Hromkovic, B. Monien, The Bisection Problem for Graphs of Degree 4 (Configuring Transputer Systems), manuscript 1990Google Scholar
  3. [Pet 1891]
    J. Petersen, Die Theorie der regulären Graphen, Acta Mathematica 15 (1891), 193–220Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Andreas Brandstädt
    • 1
  1. 1.FB 11-Mathematik FG InformatikUniversität/Gesamthochschule DuisburgGermany

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