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- JOHN MACHACEK
- 2011

The critical group K(G) of a graph G is a finite abelian group whose order is the number of spanning forests of the graph. Here we investigate the relationship between the critical group of a regular bipartite graph G and its line graph line G. The relationship between the two is known completely for regular nonbipartite graphs. We compute the critical… (More)

- Carolina Benedetti, Joshua Hallam, John Machacek
- SIAM J. Discrete Math.
- 2016

- John Machacek, Shafiu Jibrin
- J. Applied Mathematics
- 2012

- John Machacek
- Electr. J. Comb.
- 2017

We define a new type of vertex coloring which generalizes vertex coloring in graphs, hypergraphs, and simplicial complexes. This coloring also generalizes oriented coloring, acyclic coloring, and star coloring. There is an associated symmetric function in noncommuting variables for which we give a deletion-contraction formula. In the case of graphs this… (More)

- John Machacek
- Journal of Automata, Languages and Combinatorics
- 2017

We consider the language consisting of all words such that it is possible to obtain the empty word by iteratively deleting powers. It turns out that in the case of deleting squares in binary words this language is regular, and in the case of deleting squares in words over a larger alphabet the language is not regular. However, for deleting squares over any… (More)

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