...lem pairs. We prove that the problem of deciding which pairs (P, A) are generalized multi Skolem pairs is N P-complete. The proof is a reduction from the N P-complete problem Multiple Choice Matching =-=[2]-=-. We refer the reader to Garey and Johnson [2] for an in-depth treatment of the theory of N P-completeness. 2 N P-completeness of Generalized multi Skolem sequences We prove that Generalized Multi Sko...

...t. A set A that can be used to construct Skolem sequences is called a Skolem set. The existence question of deciding which sets of the form A = {1,... ,n} are Skolem sets was solved by Thoralf Skolem =-=[6]-=- in 1957. Many generalizations of Skolem sequences have been studied. In this paper we prove that the existence question for generalized multi Skolem sequences is N P-complete. This can be seen as an ...

.... One reason for them being so well studied is that they have important applications in several branches of mathematics; Shalaby [5] describes applications in design theory and graph labelings. Baker =-=[1]-=- introduced generalized Skolem sequences and used them to construct k-extended Skolem sequences. They have also been used in the construction of extended Langford sequences with small defects [3]. A g...

...aker [1] introduced generalized Skolem sequences and used them to construct k-extended Skolem sequences. They have also been used in the construction of extended Langford sequences with small defects =-=[3]-=-. A generalized Skolem sequence is a sequence of positive integers and null symbols such that an integer appears exactly twice or not at all, and the two appearances of an integer j are j positions ap...

...erent aspects and generalizations of Skolem sequences have been studied. One reason for them being so well studied is that they have important applications in several branches of mathematics; Shalaby =-=[5]-=- describes applications in design theory and graph labelings. Baker [1] introduced generalized Skolem sequences and used them to construct k-extended Skolem sequences. They have also been used in the ...