## 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. Furt
Planar Crossing Numbers of Graphs of Bounded Genus
✍ Scribed by Djidjev, Hristo N.; Vrt’o, Imrich
- Book ID
- 113044321
- Publisher
- Springer
- Year
- 2012
- Tongue
- English
- Weight
- 741 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0179-5376
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract The __crossing number__, cr(__G__), of a graph __G__ is the least number of crossing points in any drawing of __G__ in the plane. According to the Crossing Lemma of M. Ajtai, V. Chvátal, M. Newborn, E. Szemerédi, Theory and Practice of Combinatorics, North‐Holland, Amsterdam, New York,
For a given planar graph G with a set A of independent vertices, we provide a best-possible upper bound for the minimum cyclomatic number of connected induced subgraphs of G containing A. The extremal graphs are also characterized. @
The problem of determining the domination number of a graph is a well known NPhard problem, even when restricted to planar graphs. By adding a further restriction on the diameter of the graph, we prove that planar graphs with diameter two and three have bounded domination numbers. This implies that