349 research outputs found
On the algorithmic complexity of twelve covering and independence parameters of graphs
The definitions of four previously studied parameters related to total coverings and total matchings of graphs can be restricted, thereby obtaining eight parameters related to covering and independence, each of which has been studied previously in some form. Here we survey briefly results concerning total coverings and total matchings of graphs, and consider the aforementioned 12 covering and independence parameters with regard to algorithmic complexity. We survey briefly known results for several graph classes, and obtain new NP-completeness results for the minimum total cover and maximum minimal total cover problems in planar graphs, the minimum maximal total matching problem in bipartite and chordal graphs, and the minimum independent dominating set problem in planar cubic graphs
Super-simple directed designs and their smallest defining sets with its application in LDPC codes
In this paper, we show that for all (mod 5) and ,
there exists a super-simple directed design, also for these
parameters there exists a super-simple directed design such that its
smallest defining sets contain at least half of its blocks. Also, we show that
these designs are useful in constructing parity-check matrices of LDPC codes.Comment: arXiv admin note: substantial text overlap with arXiv:1508.0009
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