The Influence of the Bounded Component for the Complement in a Starshaped Orthogonal Polygon on its Kernel


Abstract in English

Many mathematicians were interested in specifying the kernel of the starshaped set. In staircase visibility the researcher Rajeev Motwani proved that the points of separating regions with dents cannot see each other, and then he proved that these points are seen from other points of an orthogonal polygon. After that Breen could find a way for specifying the kernel of starshaped orthogonal polygon when this orthogonal polygon is simply connected. The aim of this paper is to generalize the previous way when the closed orthogonal polygon is secondly connected and the bounded component for the complement contains one staircase path or two staircase paths, every path consists of more than two edges. We will prove that the kernel is either one component or two or three ones.

References used

TORANZOS,F.A. Radial functions of convex and star-shaped bodies. Am.Math.Monthly , Vol. 74, 1967, 278–280
BREEN,M. Staircase kernels in orthogonal polygons. Arch. Math, Vol.59, 1992,588-594
MOTWANI,R.؛RAGHUNATHAN,A.؛SARAN,H. Covering orthogonal polygons with star polygons: The Perfect Graph Approach. J.Comput.System Sci,Vol.40,1990,19- 48

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