11 citations · 27 across the 16 of their papers we have counts for
7 papers · 1 filter
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…
A new view of hypercube genus
Richard H. Hammack, Paul C. Kainen
Beineke, Harary and Ringel discovered a formula for the minimum genus of a torus in which the -dimensional hypercube graph can be embedded. We give a new proof of the formula by…
Graph embeddings with no Hamiltonian extensions
Paul C. Kainen, Shannon Overbay
We show that extending an embedding of a graph in a surface to an embedding of a Hamiltonian supergraph can be blocked by certain planar subgraphs but, for some subdivisions of…
Canonical Sphere Bases for Simplicial and Cubical Complexes
Paul C. Kainen
Sphere-bases are constructed for the vector space formed by the -dimensional subcomplexes, of -simplex (or -cube), for which every -face is contain…
Bochner integrals and neural networks
Paul C. Kainen, A. Vogt
A Bochner integral formula is derived that represents a function in terms of weights and a parametrized family of functions. Comparison is made to pointwise formulations, norm ineq…
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…