Elsevier

Discrete Applied Mathematics

Volume 193, 1 October 2015, Pages 180-186
Discrete Applied Mathematics

Cycles in complementary prisms

https://doi.org/10.1016/j.dam.2015.04.016Get rights and content
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Abstract

The complementary prism GG¯ of a graph G arises from the disjoint union of G and the complement G¯ of G by adding a perfect matching joining corresponding pairs of vertices in G and G¯. Partially answering a question posed by Haynes et al. (2007) we provide an efficient characterization of the circumference of the complementary prism TT¯ of a tree T and show that TT¯ has cycles of all lengths between 3 and its circumference. Furthermore, we prove that for a given graph of bounded maximum degree it can be decided in polynomial time whether its complementary prism is Hamiltonian.

Keywords

Complementary prism
Prism
Hamiltonian
Pancyclic

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