Given a weighted undirected graph G and a nonnegative integer k, the maximum k-star colorable subgraph problem consists of finding an induced subgraph of G which has maximum weight and can be star colored with at most k colors; a star coloring does not color adjacent nodes with the same color and avoids coloring any 4-path with exactly two colors. In this article, we investigate the polyhedral ...

We show some estimates for the logarithmic mean that are obtained from operator inequalities between the Barbour path and the Heinz means.

This paper gives a numerical algorithm able to compute the number of path-connected components of a set S defined by nonlinear inequalities. This algorithm uses interval analysis to create a graph which has the same number of connected components as S. An example coming from robotics is presented to illustrate the interest of this algorithm for path-planning.

We extend the work of Letchford [Letchford, A. N. 2000. Separating a superclass of comb inequalities in planar graphs. Math. Oper. Res. 25 443–454] by introducing a new class of valid inequalities for the traveling salesman problem, called the generalized domino-parity (GDP) constraints. Just as Letchford’s domino-parity constraints generalize comb inequalities, GDP constraints generalize the m...

The path, the wheelbarrow, and the bicycle inequalities have been shown by Cornuéjols, Fonlupt, and Naddef to be facetdefining for the graphical relaxation of STSP n , the polytope of the symmetric traveling salesman problem on an n-node complete graph. We show that these inequalities, and some generalizations of them, define facets also for STSP n . In conclusion, we characterize a large famil...

This paper shows how valid inequalities based on the mixing set can be used in a mixed integer programming (MIP) solver. It discusses the relation of mixing inequalities to flow path and mixed integer rounding inequalities and how currently used separation algorithms already generate cuts implicitly that can be seen as mixing cuts. Further on, it describes two new separation algorithms that gen...

We describe a stochastic network interdiction model for locating sensors that detect nuclear material. A nuclear material smuggler selects a path through a transportation network that maximizes the probability of avoiding detection. An interdictor installs sensors to minimize that maximum probability. We formulate this problem as a bi-level stochastic mixed-integer program, and then focus on a ...