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The complementary prism GḠ arises from the disjoint union of the graph G and its complement Ḡ by adding the edges of a perfect matching joining pairs of corresponding vertices of G and Ḡ. The classical problems of graph theory, clique and independent set were proved NP-complete when the input graph is a complemantary prism. In this work, we study the complexity of both problems in complementary prisms graphs from the parameterized complexity point of view. First, we prove that these problems have a kernel and therefore are Fixed-Parameter Tractable (FPT). Then, we show that both problems do not admit polynomial kernel.

Complexidade Parametrizada de Cliques e Conjuntos Independentes em Grafos Prismas Complementares