About Edge Independent Sets in Hypergraphs

D. K. Thakkar¹ , V. R. Dave²

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.5 , pp.77-81, Oct-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.7781

Online published on Oct 31, 2018

Copyright © D. K. Thakkar , V. R. Dave . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper we have introduced maximum edge independent sets in hypergraphs where a maximum edge independent set is an edge independent set with maximum cardinality. We have proved that the edge independence number of a hypergraph (with minimum edge degree at least two) remain same or decreases when an edge is removed from the hypergraph. In particular we have proved that the edge independence number of a hypergraph (with minimum edge degree at least two and edge independence number is greater than one) decreases if and only if there is a maximum edge independent set which contains the edge. We have also considered the edge independence numbers of the subhypergraph and the partial subhypergraph obtained by removing a vertex from the hypergraph. We observe that edge independence number of the finite projective plane always increases when any vertex is removed from the hypergraph and the subhypergraph is considered and the edge independence number remains same when any vertex is removed and the partial subhypergraph is considered.

Key-Words / Index Term :
Hypergraph, Edge Independent Set, Maximal Edge Independent Set, Maximum Edge Independent Sets, Edge Independence Number, Subhypergraphs, Partial Subhypergraphs

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