4 papers · 2 filters
On the zero-free region for the chromatic polynomial of graphs with maximum degree and girth
Paula M. S. Fialho, Emanuel Juliano, Aldo Procacci
The purpose of the present paper is to provide, for all pairs of integers with $\D\ge 3$ and , a positive number such that chromatic polynomial o…
A remark on the Whitney Broken Circuit Theorem
Paula M. S. Fialho, Emanuel Juliano, Aldo Procacci
In the present note we show, via the connection between chromatic polynomial and Potts model, that the Whitney Broken circuit theorem is in fact a special case of a more general id…
Forbidden subdivision in integral trees
Emanuel Juliano
We show that if all the eigenvalues of a tree are integers, then it does not contain a subdivided edge with 7 vertices.
Spectral upper bounds for the Grundy number of a graph
Thiago Assis, Gabriel Coutinho, Emanuel Juliano
The Grundy number of a graph is the minimum number of colors needed to properly color the graph using the first-fit greedy algorithm regardless of the initial vertex ordering. Comp…