Crossing numbers of sequences of graphs II: Planar tiles
Benny Pinontoan, R. Bruce Richter · Journal of Graph Theory · 2003
Abstract We describe a method of creating an infinite family of crossing‐critical graphs from a single small planar map, the tile , by gluing together many copies of the tile together in a circular fashion. This method yields all known infinite families of k ‐crossing‐critical graphs. Furthermore, the method yields new infinite families, which extend from (4,6) to (3.5,6) the interval of rationals r for which there is, for some k , an infinite sequence of k ‐crossing‐critical graphs all having average degree r . © 2003 Wiley Periodicals, Inc. J Graph Theory 42: 332–341, 2003