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Theory of Computing Systems

, Volume 31, Issue 6, pp 629–662 | Cite as

Edge-Packing in Planar Graphs

  • L. S. Heath
  • J. P. C. Vergara

Abstract.

Maximum G Edge-Packing (EPack G ) is the problem of finding the maximum number of edge-disjoint isomorphic copies of a fixed guest graph G in a host graph H . This paper investigates the computational complexity of edge-packing for planar guests and planar hosts. Edge-packing is solvable in polynomial time when both G and H are trees. Edge-packing is solvable in linear time when H is outerplanar and G is either a 3-cycle or a k -star (a graph isomorphic to K 1,k ). Edge-packing is NP-complete when H is planar and G is either a cycle or a tree with \(\geq 3\) edges. A strategy for developing polynomial-time approximation algorithms for planar hosts is exemplified by a linear-time approximation algorithm that finds a k -star edge-packing of size at least half the optimal.

Keywords

Computational Complexity Approximation Algorithm Polynomial Time Planar Graph Linear Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1998

Authors and Affiliations

  • L. S. Heath
    • 1
  • J. P. C. Vergara
    • 2
  1. 1.Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0106, USA heath@cs.vt.eduUS
  2. 2.Department of Information Systems and Computer Science, Ateneo De Manila University, Manila 0917, Philippines jpv@admu.edu.phPH

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