Edge-Packing in Planar Graphs

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.

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Received May 1995, and in revised form November 1995, and in final form December 1997.

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Heath, L., Vergara, J. Edge-Packing in Planar Graphs. Theory Comput. Systems 31, 629–662 (1998). https://doi.org/10.1007/s002240000107

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Keywords

  • Computational Complexity
  • Approximation Algorithm
  • Polynomial Time
  • Planar Graph
  • Linear Time