Bounds of graph parameters for global constraints

Bounds for the Co-PI index of a graph

In this paper, we present some inequalities for the Co-PI index involving the some topological indices, the number of vertices and edges, and the maximum degree. After that, we give a result for trees. In addition, we give some inequalities for the largest eigenvalue of the Co-PI matrix of G.

Graph Coloring with Local and Global Constraints Graph Coloring with Local and Global Constraints

Best Monotone Degree Bounds for Various Graph Parameters

We identify best monotone degree bounds for the chromatic number and independence number of a graph. These bounds are best in the same sense as Chvátal’s hamiltonian degree condition. 1 Terminology and Notation We consider only undirected graphs without loops or multiple edges. Our terminology and notation will be standard except as indicated, and a good reference for any undefined terms is [14...

Lower Bounds for Approximating Graph Parameters via Communication Complexity

In a celebrated work, Blais, Brody, and Matulef [5] developed a technique for proving property testing lower bounds via reductions from communication complexity. Their work focused on testing properties of functions, and yielded new lower bounds as well as simplified analyses of known lower bounds. Here, we take a further step in generalizing the methodology of [5] to analyze the query complexi...

Acquiring Parameters of Implied Global Constraints

This paper presents a technique for learning parameterized implied constraints. They can be added to a model to improve the solving process. Experiments on implied Gcc constraints show the interest of our approach.