Thickness-two graphs part one: New nine-critical graphs, permuted layer graphs, and Catlin's graphs

نویسندگان

  • Debra L. Boutin
  • Ellen Gethner
  • Thom Sulanke
چکیده

The purpose of this paper is to offer new insight and tools toward the pursuit of the largest chromatic number in the class of thickness-two graphs. At present, the highest chromatic number known for a thickness-two graph is 9, and there is only one known color-critical 1 such graph. We introduce 40 small 9-critical thickness-two graphs, and then use a new construction, the permuted layer graphs, together with a construction of Hajós to create an infinite family of 9-critical thickness-two graphs. Finally, a non-trivial infinite subfamily of Catlin's graphs, with directly computable chromatic numbers, is shown to have thickness two.

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عنوان ژورنال:
  • Journal of Graph Theory

دوره 57  شماره 

صفحات  -

تاریخ انتشار 2008