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


Maximum G Edge-Packing (EPackG ) 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 K1,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.

Copyright information

© 1998 Springer-Verlag New York Inc.

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

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