11 citations · 11 across the 9 of their papers we have counts for
9 papers
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 crossing nu…
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…
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…
All bipartite circulants are dispersable
Shannon Overbay, Samuel Joslin, Paul C. Kainen
We show that a cyclic vertex order due to Yu, Shao and Li gives a dispersable book embedding for any bipartite circulant.
Eulerian 2-Complexes
Richard H. Hammack, Paul C. Kainen
It is shown that Euler's theorem for graphs can be generalized for 2-complexes. Two notions that generalize cycle and Eulerian tour are introduced (``circlet'' and ``Eulerian cover…
Euler's Theorem for Regular CW-Complexes
Richard H. Hammack, Paul C. Kainen
For strongly connected, pure -dimensional regular CW-complexes, we show that {\it evenness} (each -cell is contained in an even number of -cells) is equivalent to ge…