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Clique Vertex Magic Cover of a Graph

✍ Scribed by K. A. Sugeng; J. Ryan


Book ID
107508949
Publisher
Springer-Verlag
Year
2011
Tongue
English
Weight
312 KB
Volume
5
Category
Article
ISSN
1661-8270

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The following conjecture of T. Gallai is proved: If G is a chordal graph on n vertices, such that all its maximal complete subgraphs have order at least 3, then there is a vertex set of cardinality ~n/3 which meets all maximal complete subgraphs of G. Further related results are given.

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The following problem is investigated. Given an undirected graph G, determine the smallest cardinality of a vertex set that meets all complete subgraphs KC G maximal under inclusion.