Displaying similar documents to “On bounded paradoxical subsets of the plane”

5-Stars of Low Weight in Normal Plane Maps with Minimum Degree 5

Oleg V. Borodin, Anna O. Ivanova, Tommy R. Jensen (2014)

Discussiones Mathematicae Graph Theory

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It is known that there are normal plane maps M5 with minimum degree 5 such that the minimum degree-sum w(S5) of 5-stars at 5-vertices is arbitrarily large. In 1940, Lebesgue showed that if an M5 has no 4-stars of cyclic type (5, 6, 6, 5) centered at 5-vertices, then w(S5) ≤ 68. We improve this bound of 68 to 55 and give a construction of a (5, 6, 6, 5)-free M5 with w(S5) = 48

On the Vertex Separation of Cactus Graphs

Markov, Minko (2007)

Serdica Journal of Computing

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This paper is part of a work in progress whose goal is to construct a fast, practical algorithm for the vertex separation (VS) of cactus graphs. We prove a theorem for cacti", a necessary and sufficient condition for the VS of a cactus graph being k. Further, we investigate the ensuing ramifications that prevent the construction of an algorithm based on that theorem only.