Gallai Theorems Involving Domination Parameters

In 1959 Gallai [5] showed that the vertex independence number and the vertex covering number of a graph G = (V,E) sum to |V |. Over the last twenty years, many results similar to Gallai’s Theorem have been observed [3]. These theorems are referred to as “Gallai Theorems” and usually have the form: α+ β = n. Slater [17] described several graph subset parameters using linear programs (LP) and integer programs. Gallai Theorems for the resulting parameters may be obtained by using the concepts of LPduality and complementarity. Slater defines several of the parameters ∗This work was done while the author visited Clemson University.