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math.CO2016
Gallai's path decomposition conjecture for graphs of small maximum degree
Marthe Bonamy, Thomas Perrett
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 g…
math.CO2016★ 1 cited
Density of Zeros of the Tutte Polynomial
Seongmin Ok, Thomas J. Perrett
The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the zeros o…
math.CO2016
Chromatic roots and minor-closed families of graphs
Thomas Perrett
Given a minor-closed class of graphs , what is the infimum of the non-trivial roots of the chromatic polynomial of ? When is the class…