تهتم نظرية المجموعات النجمية بتعيين نواة المجموعة النجمية و أيضاً رؤية النقاط و المناطق لبعضها البعض، ففي حالة الرؤية الدرجية برهن الباحث راجيف موتواني أن نقاط المناطق المفصولة عن بعضها بالأغوار لا ترى بعضها بعضاً، و بعد ذلك تمكنت الباحثة مارلين برين من إيجاد طريقة لتعيين نواة المضلع المتعامد النجمي درجياً عندما يكون المضلع المتعامد بسيط الترابط.
في هذا البحث سوف نعمم الطريقة السابقة عندما يكون المضلع المتعامد المغلق ثنائي الترابط، و جبهة المركبة المحدودة للمتممة اجتماعاً لثلاث ممرات درجية كل منها مؤلف من أكثر من ضلعين، و سنثبت أن النواة تتألف من مركبة واحدة فقط.
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
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 po
The staircase visibility concerns with the study of orthogonal polygon, one of the most important subjects which are studied is the Specification kernel of the orthogonal starshaped set. Toranzos represent a very important result in Specifying the ke
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