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.
Paul, Alice, Pippenger, Nicholas (2011)
The Electronic Journal of Combinatorics [electronic only]
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Bohdan Zelinka (1967)
Matematický časopis
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Bouttier, J., Di Francesco, P., Guitter, E. (2004)
The Electronic Journal of Combinatorics [electronic only]
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Zdzisław Skupień, Władysław Zygmunt (1980)
Fundamenta Mathematicae
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Van Bussel, Frank (2002)
The Electronic Journal of Combinatorics [electronic only]
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Bohdan Zelinka (1976)
Czechoslovak Mathematical Journal
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Liu, Qi, West, Douglas B. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Markov, Minko (2008)
Serdica Journal of Computing
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We investigate the NP-complete problem Vertex Separation (VS) on Maximal Outerplanar Graphs (mops). We formulate and prove a “main theorem for mops”, a necessary and sufficient condition for the vertex separation of a mop being k. The main theorem reduces the vertex separation of mops to a special kind of stretchability, one that we call affixability, of submops.