11 citations · 27 across the 16 of their papers we have counts for
6 papers · 1 filter
Book embeddings of graphs and a theorem of Whitney
Paul C. Kainen, Shannon Overbay
It is shown that the number of pages required for a book embedding of a graph is the maximum of the numbers needed for any of the maximal nonseparable subgraphs and that a plane gr…
On dispersability of some circulant graphs
Paul C. Kainen, Samuel S. Joslin, Shannon Overbay
The matching book thickness of a graph is the least number of pages in a book embedding such that each page is a matching. A graph is dispersable if its matching book thickness equ…
On dispersability of some products of cycles
Samuel S. Joslin, Paul C. Kainen, Shannon Overbay
We show that the matching book thickness of the Cartesian product of two odd-length cycle-graphs is five if at least one of the cycles has length 3 or 5.
Factorization of Platonic Polytopes into canonical spheres
R. H. Hammack, P. C. Kainen
Factorization into spheres is achieved for skeleta of the simplex, cube, and cross-polytope, both explicitly and using Keevash's proof of existence of designs.
Cubic planar bipartite graphs are dispersable
Paul C. Kainen, Shannon Overbay
A graph is called dispersable if it has a book embedding in which each page has maximum degree 1 and the number of pages is the maximum degree. Bernhart and Kainen conjectured ever…
Lunaport: Math, Mechanics & Transport
Paul C. Kainen
Issues for transport facilities on the lunar surface related to science, engineering, architecture, and human-factors are discussed. Logistic decisions made in the next decade may…