Generalized limited packings of some graphs with a limited number of P_4-partners

M.P. DOBSON; E. HINRICHSEN; V. LEONI

THEORETICAL COMPUTER SCIENCE

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2014

0304-3975

By using modular decomposition and handling certain graph operations such as join and union, we show that the Generalized Limited Packing Problem ---NP-complete in general-- can be solved in polynomial time in some graph classes with a limited number of $P_4$-partners; specifically $P_4$-tidy graphs, which contain cographs and $P_4$-sparse graphs. In particular, we describe an algorithm to compute the associated numbers in polynomial time within these graph classes. In this way, we generalize some of the previous results on the subject.We also  make some progress on the study of the computational complexity of the Generalized Multiple Domination Problem in graphs.