# Thomas Perrett

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- Marthe Bonamy, Thomas Perrett
- ArXiv
- 2016

Gallai’s path decomposition conjecture states that the edges of any connected graph on n vertices can be decomposed into at most n+1 2 paths. We confirm that conjecture for all graphs with maximum degree at most five.

- Thomas Perrett
- SIAM J. Discrete Math.
- 2016

Given a minor-closed class of graphs G, what is the infimum of the non-trivial roots of the chromatic polynomial of G ∈ G? When G is the class of all graphs, the answer is known to be 32/27. We answer this question exactly for three minorclosed classes of graphs. Furthermore, we conjecture precisely when the value is larger than 32/27.

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