, Volume 45, Issue 2, pp 227-262

First online:

Recognizing Hole-Free 4-Map Graphs in Cubic Time

  • Zhi-Zhong ChenAffiliated withDepartment of Mathematical Sciences, Tokyo Denki University, Hatoyama, Saitama 350-0394 Email author 
  • , Michelangelo GrigniAffiliated withDepartment of Mathematics and Computer Science, Emory University, Atlanta, GA 30322 Email author 
  • , Christos H. PapadimitriouAffiliated withComputer Science Division, University of California at Berkeley, Berkeley, CA 94720 Email author 

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We present a cubic-time algorithm for the following problem: Given a simple graph, decide whether it is realized by adjacencies of countries in a map without holes, in which at most four countries meet at any point.

Planar graphs Maps Map graphs Cliques Graph algorithms