The relation between the staircase kernel and the position of the three staircase paths of the bounded component for the complement


Abstract in English

One of the most important subjects that the starshaped sets theory concerned withis specifying the kernel of the starshaped set and vision the points and regions for each other. So in staircase visibilitytheresearcher Rajeev Motwani proved that the points of separating regions with dents cannot see each other. After that Breen could find a way for specifying the kernel of starshaped orthogonal polygon when this orthogonal polygon is simply connected. In this paper we will generalize the previous way when the closed orthogonal polygon is secondly connected and the bounded component for the complement is union of three staircase paths, every path consists of more than two edges. We will prove that the kernel is only one component.

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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