11 citations · 11 across the 5 of their papers we have counts for
7 papers
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…
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.
Neighborhood reconstruction and cancellation of graphs
Richard H. Hammack, Cristina Mullican
We connect two seemingly unrelated problems in graph theory. Any graph has an associated neighborhood multiset whose elements are prec…
Cycle bases of reduced powers of graphs
Richard H. Hammack, Gregory D. Smith
We define what appears to be a new construction. Given a graph and a positive integer , the reduced th power of , denoted , is the configuration space in whic…
Associativity and non-associativity of some hypergraph products
Richard H. Hammack, Marc Hellmuth, Lydia Ostermeier +1
Several variants of hypergraph products have been introduced as generalizations of the strong and direct products of graphs. Here we show that only some of them are associative. In…