A Linear-Time Algorithm for Testing Outer-1-Planarity

作者：Hong Seok Hee^*; Eades Peter; Katoh Naoki; Liotta Giuseppe; Schweitzer Pascal; Suzuki Yusuke

来源：Algorithmica, 2015, 72(4): 1033-1054.

DOI：10.1007/s00453-014-9890-8

• Graph drawing
• 1-Planar graphs
• Outer 1-planar graphs
• 1-Planarity
• 1-Planar embedding

A graph is 1-planar if it can be embedded in the plane with at most one crossing per edge. It is known that the problem of testing 1-planarity of a graph is NP-complete. In this paper, we study outer-1-planar graphs. A graph is outer-1-planar if it has an embedding in which every vertex is on the outer face and each edge has at most one crossing. We present a linear time algorithm to test whether a given graph is outer-1-planar. The algorithm can be used to produce an outer-1-planar embedding in linear time if it exists.

• 出版日期2015-8