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pro vyhledávání: '"Hammack, Richard"'
Autor:
Hammack, Richard H., Kainen, Paul C.
Publikováno v:
Mathematics magazine, vol. 97, no. 1, Feb. 2024
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''), and we show that for a strongly-connected, pure 2-complex, the fo
Externí odkaz:
http://arxiv.org/abs/2401.00323
Autor:
Hammack, Richard H., Kainen, Paul C.
For strongly connected, pure $n$-dimensional regular CW-complexes, we show that {\it evenness} (each $(n{-}1)$-cell is contained in an even number of $n$-cells) is equivalent to generalizations of both cycle decomposition and traversability.
Com
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Externí odkaz:
http://arxiv.org/abs/2401.00084
Autor:
Hammack, Richard H., Kainen, Paul C.
Publikováno v:
American Math. Monthly 128 (4) (2021) 352-359
Beineke, Harary and Ringel discovered a formula for the minimum genus of a torus in which the $n$-dimensional hypercube graph can be embedded. We give a new proof of the formula by building this surface as a union of certain faces in the hypercube's
Externí odkaz:
http://arxiv.org/abs/2401.00070
Publikováno v:
In International Journal of Greenhouse Gas Control July 2023 127
Publikováno v:
Electron. J. Combin. 24 (2017), no. 2, Paper 2.8, 11 pp
We connect two seemingly unrelated problems in graph theory. Any graph $G$ has an associated neighborhood multiset $\mathscr{N}(G)= \{N(x) \mid x\in V(G)\}$ whose elements are precisely the open vertex-neighborhoods of $G$. In general there exist non
Externí odkaz:
http://arxiv.org/abs/1612.02717
Akademický článek
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Autor:
Hammack, Richard H., Smith, Gregory D.
We define what appears to be a new construction. Given a graph $G$ and a positive integer $k$, the reduced $k$th power of $G$, denoted $G^{(k)}$, is the configuration space in which $k$ indistinguishable tokens are placed on the vertices of $G$, so t
Externí odkaz:
http://arxiv.org/abs/1601.02896
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 addition to the Cartesian product, these are the minimal rank preserv
Externí odkaz:
http://arxiv.org/abs/1511.07162
Autor:
Hammack Richard H.
Publikováno v:
Discussiones Mathematicae Graph Theory, Vol 41, Iss 1, Pp 335-339 (2021)
Any graph G admits a neighborhood multiset 𝒩(G) = {NG(x) | x ∈ V (G)} whose elements are precisely the open neighborhoods of G. We say G is neighborhood reconstructible if it can be reconstructed from 𝒩(G), that is, if G ≅ H whenever 𝒩 (
Externí odkaz:
https://doaj.org/article/b6d41b99e517424ba394adbb9e7387da