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Displaying similar documents to “Graphs Which Are Switching Equivalent To Their Line Graphs”

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.

The ramsey number for theta graph versus a clique of order three and four

M.S.A. Bataineh, M.M.M. Jaradat, M.S. Bateeha (2014)

Discussiones Mathematicae Graph Theory

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For any two graphs F1 and F2, the graph Ramsey number r(F1, F2) is the smallest positive integer N with the property that every graph on at least N vertices contains F1 or its complement contains F2 as a subgraph. In this paper, we consider the Ramsey numbers for theta-complete graphs. We determine r(θn,Km) for m = 2, 3, 4 and n > m. More specifically, we establish that r(θn,Km) = (n − 1)(m − 1) + 1 for m = 3, 4 and n > m