13 research outputs found
Note on power hypergraphs with equal domination and matching numbers
We present some examples that refute two recent results in the literature
concerning the equality of the domination and matching numbers for power and
generalized power hypergraphs. In this note we pinpoint the flaws in the proofs
and suggest how they may be mended.Comment: 7 pages, 1 figure, XIII Encuentro Andaluz de Matem\'atica Discreta,
(C\'adiz) Spain, july, 202
Bounds for the independence number of a graph
The independence number of a graph is the maximum number of vertices from the vertex set of the graph such that no two vertices are adjacent. We systematically examine a collection of upper bounds for the independence number to determine graphs for which each upper bound is better than any other upper bound considered. A similar investigation follows for lower bounds. In several instances a graph cannot be found. We also include graphs for which no bound equals and bounds which do not apply to general graphs