11 citations · 11 across the 4 of their papers we have counts for
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math.CO2023
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…
math.CO2023★ 11 cited
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…
math.CO2021
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.