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- J W Chaffee
- IEEE transactions on ultrasonics, ferroelectrics…
- 1987

- Joe Chaffee, Christopher A. Rodger
- Discrete Mathematics
- 2013

- Joe Chaffee, Matt Noble
- Australasian J. Combinatorics
- 2016

The dimension of a graph G is defined to be the minimum n such that G has a representation as a unit-distance graph in R. A problem posed by Paul Erdős asks for the minimum number of edges in a graph of dimension 4. In a recent article, R. F. House showed that the answer to Erdős’ question is 9. In this article, we give a shorter (and we feel more… (More)

- John Asplund, Joe Chaffee, James M. Hammer
- Graphs and Combinatorics
- 2017

- Joe Chaffee
- Australasian J. Combinatorics
- 2014

A cover (with triples) of λK n is an ordered pair (V, B) where V is an n-element set and B is a set of 3-element subsets of V called blocks such that each 2-element subset of V appears in at least λ blocks. Define The excess (sometimes called the padding) of a cover is defined to be E(B) − E(λK n), although it is often convenient to think of the excess as… (More)

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