5 papers
Sunlet factors for Cartesian products of cycles
Henry Jervis, Paul C. Kainen
A sunlet is a cycle with a pendant edge attached at each vertex of the cycle. For the bipartite toroidal grid graphs , factorizations into sunlets are given by…
Skewness, crossing number and Euler's bound for graphs on surfaces
Paul C. Kainen
For every connected graph and surface , we consider the well-known string of inequalities , where and denote skewness and crossi…
Star arboricity relaxed book thickness of
Paul C. Kainen
A book embedding of the complete graph needs pages and the page-subgraphs can be chosen to be spanning paths (for even) and one spanning star…
Construction numbers: How to build a graph?
Paul C. Kainen
A construction sequence for a graph is a listing of the elements of the graph (the set of vertices and edges) such that each edge follows both its endpoints. The construction numbe…
Complexity of graph evolutions
Jeffrey Gao, Paul C. Kainen
A permutation of the elements of a graph is a {\it construction sequence} if no edge is listed before either of its endpoints. The complexity of such a sequence is investigated by…