1 citations · 3 across the 4 of their papers we have counts for
5 papers · 1 filter
Colouring Graphs with Sparse Neighbourhoods: Bounds and Applications
Marthe Bonamy, Thomas Perrett, Luke Postle
Let be a graph with chromatic number , maximum degree and clique number . Reed's conjecture states that for…
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…
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…
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…
A zero-free interval for chromatic polynomials of graphs with 3-leaf spanning trees
Thomas Perrett
It is proved that if is a graph containing a spanning tree with at most three leaves, then the chromatic polynomial of has no roots in the interval , where $t_1 \a…