6 papers · 1 filter
Tightness of a MaxCut Lower Bound via Vector Chromatic Number
Emanuel Juliano
Recently, Balla, Janzer, and Sudakov showed a lower bound on the MaxCut in terms of the vector chromatic number, recovering known results on the MaxCut of -free graphs. In this…
The edge-isoperimetric number of graphs and their powers: approaches from spectral graph theory, optimization and finite geometry
Aida Abiad, Nils van de Berg, Emanuel Juliano +4
We obtain several sharp spectral bounds, approximations, and exact values for the isoperimetric number and related edge-expansion parameters of graphs. Our results focus on graph p…
A graph energy conjecture through the lenses of semidefinite programming
Aida Abiad, Gabriel Coutinho, Emanuel Juliano +1
Let be a graph on vertices with independence number . Let be the energy of a graph, defined as the sum of the absolute values of the adjacency eigen…
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 …
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.