We o er a formulation that locates hubs on a network in a competitive environment; that is, customer capture is sought, which happens whenever the location of a new hub results in a reduction of the current cost (time, distance) needed by the tra c that goes from the speci ed origin to the speci ed destination. The formulation presented here reduces the number of variables and constraints as co...

A graph is called $P_t$-free if it does not contain a $t$-vertex path as an induced subgraph. While $P_4$-free graphs are exactly cographs, the structure of for $t \geqslant 5$ remains little understood. On one hand, classic computational problems such Maximum Weight Independent Set (MWIS) and $3$-Coloring known to be NP-hard on any fixed $t$. other despite significant effort, polynomial-time a...

This paper introduces a general modeling framework for multi-type maximal covering location problem in which the position of facilities different normed spaces are simultaneously decided to maximize demand generated by set points. From need intertwining decisions discrete and continuous sets, hybridized is considered some types be located finite sets others spaces. A natural non-linear model pr...

Let CS denote the class of groups isomorphic to the fundamental group of two closed hyperbolic surfaces identified along an essential simple closed curve in each. We construct a bi-Lipschitz map between the universal covers of these spaces equipped with a CAT(−1) metric, proving all groups in CS are quasi-isometric. The class CS has infinitely many abstract commensurability classes, which we ch...

In Section 2 of [1] C. Huybrechts introduces the notion of covers and quotients of dimensional dual hyperovals and calls maximal covers universal. S. Yoshiara [2] and [3] calls such maximal covers simply connected. Given a dimensional dual hyperoval, one may ask, if there exists a unique (simply connected) maximal cover of the given dual hyperoval. We shall show, that this is true. We also show...