Compact visibility representation of 4-connected plane graphs

  • Authors:

  • Xin He;Jiun-Jie Wang;Huaming Zhang

  • Affiliations:

  • Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, NY 14260, United States;Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, NY 14260, United States;Department of Computer Science, The University of Alabama in Huntsville, Huntsville, AL 35899, United States

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2012

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Abstract

The visibility representation (VR for short) is a classical representation of plane graphs. The VR has various applications and has been extensively studied in the literature. A main focus of the study is to minimize the size of the VR. It is known that there exists a plane graph G with n vertices where any VR of G requires a size at least @?2n3@?x(@?4n3@?-3). For upper bounds, it is known that every plane graph has a VR with size at most @?23n@?x(2n-5), and a VR with size at most (n-1)x@?43n@?. It has been an open problem to find a VR with both height and width simultaneously bounded away from the trivial upper bounds (namely of size c"hnxc"wn with c"h