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Extremal Point and Edge Sets in n-Graphs
Published online by Cambridge University Press: 20 November 2018
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A set of points (edges) of a graph is independent if no two distinct members of the set are adjacent. Gallai (1) observed that, if A0 (B0) is the minimum number of points (edges) of a finite graph covering all the edges (points) and A1 (B1) is the maximum number of independent points (edges), then:
holds, where m is the number of points of the graph.
The concepts of independence and covering are generalized in various ways for n-graphs. In this paper we establish certain connections between the corresponding extreme numbers analogous to the above result of Gallai.
Ray-Chaudhuri considered (2) independence and covering problems in n-graphs and determined algorithms for finding the minimal cover and some associated numbers.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1969
References
1.
Gallai, T., Über extreme Punkt- und Kantenmengen, Ann. Univ. Sci. Budapest Eôtvôs Sect. Math.
2 (1959), 133–138.Google Scholar
2.
Ray-Chaudhuri, D. K., An algorithm for a minimum cover of an abstract complex, Can. J. Math.
15 (1963), 11–24.Google Scholar
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