A fraction-free unit-circle zero location test for a polynomial with any singularity profile

2018 ◽  
Vol 67 (7) ◽  
pp. 1420-1459 ◽  
Author(s):  
Alexander Lifshitz ◽  
Yuval Bistritz
Keyword(s):  
Unit Circle ◽  
Zero Location ◽  
Location Test

The Restricted Arc-Width of a Graph

10.37236/1734 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
David Arthur
Keyword(s):  
Unit Circle ◽  
Single Point ◽  
Minimum Width ◽  
Graph Operations ◽  
Function Mapping

An arc-representation of a graph is a function mapping each vertex in the graph to an arc on the unit circle in such a way that adjacent vertices are mapped to intersecting arcs. The width of such a representation is the maximum number of arcs passing through a single point. The arc-width of a graph is defined to be the minimum width over all of its arc-representations. We extend the work of Barát and Hajnal on this subject and develop a generalization we call restricted arc-width. Our main results revolve around using this to bound arc-width from below and to examine the effect of several graph operations on arc-width. In particular, we completely describe the effect of disjoint unions and wedge sums while providing tight bounds on the effect of cones.

Sign in / Sign up

Export Citation Format

Share Document