Four-connected spanning subgraphs of doughnut graphs

  • Authors:

  • Md. Rezaul Karim;Md. Saidur Rahman

  • Affiliations:

  • Dept. of Computer Science and Engineering, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh and Dept. of Computer Science and Engineering, University of Dhaka, Dhaka, Banglad ...;Dept. of Computer Science and Engineering, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh

  • Venue:
  • WALCOM'08 Proceedings of the 2nd international conference on Algorithms and computation
  • Year:
  • 2008

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Abstract

The class doughnut graphs is a subclass of 5-connected planar graphs. In a planar embedding of a doughnut graph of n vertices there are two vertex-disjoint faces each having exactly n/4 vertices and each of all the other faces has exactly three vertices. Recently the class of doughnut graphs is introduced to show that a graph in this class admits a straight-line grid drawing with linear area and hence any spanning subgraph of a doughnut graph also admits a straight-line grid drawing with linear area. But recognition of a spanning subgraph of a doughnut graph is a non-trivial problem, since recognition of a spanning subgraph of a given graph is an NP-complete problem in general. In this paper, we establish a necessary and sufficient condition for a 4-connected planar graph G to be a spanning subgraph of a doughnut graph. We also give a linear-time algorithm to augment a 4-connected planar graph G to a doughnut graph if G satisfies the necessary and sufficient condition.